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Journal articles on the topic 'Viscosity approximation methods'

Author: Grafiati

Published: 3 June 2025

Last updated: 13 July 2025

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1

Xu, Hong-Kun. "Viscosity approximation methods for nonexpansive mappings." Journal of Mathematical Analysis and Applications 298, no. 1 (2004): 279–91. http://dx.doi.org/10.1016/j.jmaa.2004.04.059.

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2

Frimpong, K., and E. Prempeh. "Viscosity Approximation Methods in Reflexive Banach Spaces." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–11. http://dx.doi.org/10.9734/bjmcs/2017/33396.

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3

Song, Yisheng, and Rudong Chen. "Viscosity approximation methods for nonexpansive nonself-mappings." Journal of Mathematical Analysis and Applications 321, no. 1 (2006): 316–26. http://dx.doi.org/10.1016/j.jmaa.2005.07.025.

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4

Wu, XianBing, and LeiNa Zhao. "Viscosity Approximation Methods for Multivalued Nonexpansive Mappings." Mediterranean Journal of Mathematics 13, no. 5 (2015): 2645–57. http://dx.doi.org/10.1007/s00009-015-0644-x.

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5

Lou, Jian, Li-juan Zhang, and Zhen He. "Viscosity approximation methods for asymptotically nonexpansive mappings." Applied Mathematics and Computation 203, no. 1 (2008): 171–77. http://dx.doi.org/10.1016/j.amc.2008.04.018.

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6

Moudafi, A. "Viscosity Approximation Methods for Fixed-Points Problems." Journal of Mathematical Analysis and Applications 241, no. 1 (2000): 46–55. http://dx.doi.org/10.1006/jmaa.1999.6615.

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7

K., Piesie Frimpong, and Prempeh E. "Viscosity Approximation Methods in Reflexive Banach Spaces." British Journal of Mathematics & Computer Science 22, no. 2 (2017): 1–11. https://doi.org/10.9734/BJMCS/2017/33396.

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In this paper, we study viscosity approximation methods in reflexive Banach spaces. Let X be a reflexive Banach space which admits a weakly sequentially continuous duality mapping <em>j : X → X<sup>*</sup>, C</em> a nonempty closed convex subset of <em>X, h<sub>n</sub></em>, where n ≥1 a sequence of contractions on C and Tn, n = 1; 2; 3; N, for N 2 N, a nite family of commuting nonexpansive mappings on C. We show that under appropriate conditions on n the explicit iterative sequence n de ned by n+1 = nhn(n) + (1 􀀀 n)Tnn; n 1; 1 2 C where n 2 (0; 1) converges strongly to a common xed point 2 NT k=1 Fk : We consequently show that the results is true for an in nite family Tn; n = 1; 2; 3; of commuting nonexpansive mapping on C.

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8

Ceng, Lu-Chuan, Ching-Feng Wen, and Chin-Tzong Pang. "Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/173461.

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We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.

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9

Kumari, Mandeep, and Renu Chugh. "Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds." International Journal of Applied Mathematical Research 4, no. 2 (2015): 299. http://dx.doi.org/10.14419/ijamr.v4i2.4239.

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<p>In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.</p>

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10

Aoyama, Koji, and Yasunori Kimura. "VISCOSITY APPROXIMATION METHODS WITH A SEQUENCE OF CONTRACTIONS." Cubo (Temuco) 16, no. 1 (2014): 09–20. http://dx.doi.org/10.4067/s0719-06462014000100002.

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11

Chen, Zhe. "Generalized viscosity approximation methods in multiobjective optimization problems." Computational Optimization and Applications 49, no. 1 (2009): 179–92. http://dx.doi.org/10.1007/s10589-009-9282-1.

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12

Kohlenbach, Ulrich, and Pedro Pinto. "Quantitative translations for viscosity approximation methods in hyperbolic spaces." Journal of Mathematical Analysis and Applications 507, no. 2 (2022): 125823. http://dx.doi.org/10.1016/j.jmaa.2021.125823.

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13

Liu, Chao, and Meimei Song. "The New Viscosity Approximation Methods for Nonexpansive Nonself-Mappings." International Journal of Modern Nonlinear Theory and Application 05, no. 02 (2016): 104–13. http://dx.doi.org/10.4236/ijmnta.2016.52011.

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14

Zhang, Lijuan. "VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE SEMINGROUPS AND MONOTONE MAPPPINGS." East Asian mathematical journal 28, no. 5 (2012): 597–604. http://dx.doi.org/10.7858/eamj.2012.045.

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15

Cui, Yunan, Zuo Zhan Fei, and Henryk Hudzik. "Viscosity Approximation Methods for Multivalued Mappings in Banach Spaces." Numerical Functional Analysis and Optimization 33, no. 11 (2012): 1288–303. http://dx.doi.org/10.1080/01630563.2012.693810.

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16

Chen, Junmin, Lijuan Zhang, and Tiegang Fan. "Viscosity approximation methods for nonexpansive mappings and monotone mappings." Journal of Mathematical Analysis and Applications 334, no. 2 (2007): 1450–61. http://dx.doi.org/10.1016/j.jmaa.2006.12.088.

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17

Zegeye, Habtu, Naseer Shahzad, and Tefera Mekonen. "Viscosity approximation methods for pseudocontractive mappings in Banach spaces." Applied Mathematics and Computation 185, no. 1 (2007): 538–46. http://dx.doi.org/10.1016/j.amc.2006.07.063.

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18

Zegeye, Habtu, and Naseer Shahzad. "Viscosity approximation methods for nonexpansive multimaps in Banach spaces." Acta Mathematica Sinica, English Series 26, no. 6 (2010): 1165–76. http://dx.doi.org/10.1007/s10114-010-7521-0.

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19

Ceng, Lu-Chuan, Abdul Latif, and Abdullah E. Al-Mazrooei. "Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–18. http://dx.doi.org/10.1155/2013/328740.

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We introduce Mann-type viscosity approximation methods for finding solutions of a multivalued variational inclusion (MVVI) which are also common ones of finitely many variational inequality problems and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type viscosity approximation methods are based on the Mann iteration method and viscosity approximation method. We consider and analyze Mann-type viscosity iterative algorithms not only in the setting of uniformly convex and 2-uniformly smooth Banach space but also in a uniformly convex Banach space having a uniformly Gáteaux differentiable norm. Under suitable assumptions, we derive some strong convergence theorems. In addition, we also give some applications of these theorems; for instance, we prove strong convergence theorems for finding a common fixed point of a finite family of strictly pseudocontractive mappings and a countable family of nonexpansive mappings in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

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20

Markov, V. A., S. N. Devyanin, S. A. Zykov, and Boven' Sa. "Research of viscosity characteristics of biofuels based on vegetable oils." Traktory i sel hozmashiny 83, no. 12 (2016): 3–9. http://dx.doi.org/10.17816/0321-4443-66237.

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Depletion of oil fields and environmental deterioration demand the search of alternative sources of energy. Actuality of the article is driven by the need for increased use of alternative fuels in internal combustion engines. As advanced alternative fuels for diesel engines, the article considers fuels extracted from vegetable oils and animal fatty substances. These fuels are produced from renewable feedstocks and characterized by good environmental qualities. The advantages of use of vegetable origin fuels as motor fuel are shown. One of the problems of use of fuels based on vegetable oils is their increased viscosity. The viscosity characteristics of mixtures of petroleum diesel fuel and vegetable oils are investigated. Various vegetable oils, namely rapeseed oil, sunflower oil, soybean oil, corn oil, mustard oil, as well as oil extracted from the Pongamia Pinnata plant are considered. A method of approximation of viscosity characteristics of mixed biofuels in the form of algebraic polynomial is suggested. Experimental data on viscosity of these oils and their mixtures with petroleum diesel fuel are used in calculation researches. Approximating dependences of these experimental data with the use of the familiar logarithmic method and a suggested algebraic method are obtained. The analysis of approximation accuracy of experimental data on viscosity of biofuel is carried out with the use of mentioned methods. Parameters of the D-245.12S diesel engine operating on mixtures of rapeseed and sunflower oils with petroleum diesel fuel are presented. The effectiveness of the suggested method of approximation of viscosity characteristics of petroleum diesel fuel and vegetable oils mixtures is shown. The method is characterized by high accuracy and can be used for the approximation of viscosity characteristics of various fuel mixtures.

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21

Patel, Prashant, and Rajendra Pant. "Viscosity approximation methods for quasi-nonexpansive mappings in Banach spaces." Filomat 35, no. 9 (2021): 3113–26. http://dx.doi.org/10.2298/fil2109113p.

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In this article, we present viscosity approximation methods for finding a common point of the set of solutions of a variational inequality problem and the set of fixed points of a multi-valued quasinonexpansive mapping in a Banach space. We also discuss some examples to illustrate facts and study the convergence behaviour of the iterative schemes presented herein, numerically.

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22

Wangkeeree, Rabian. "Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert Spaces." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–10. http://dx.doi.org/10.1155/2007/48648.

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Viscosity approximation methods for nonexpansive nonself-mappings are studied. LetCbe a nonempty closed convex subset of Hilbert spaceH,Pa metric projection ofHontoCand letTbe a nonexpansive nonself-mapping fromCintoH. For a contractionfonCand{tn}⊆(0,1), letxnbe the unique fixed point of the contractionx↦tnf(x)+(1−tn)(1/n)∑j=1n(PT)jx. Consider also the iterative processes{yn}and{zn}generated byyn+1=αnf(yn)+(1−αn)(1/(n+1))∑j=0n(PT)jyn,n≥0, andzn+1=(1/(n+1))∑j=0nP(αnf(zn)+(1−αn)(TP)jzn),n≥0,wherey0,z0∈C,{αn}is a real sequence in an interval[0,1]. Strong convergence of the sequences{xn},{yn}, and{zn}to a fixed point ofTwhich solves some variational inequalities is obtained under certain appropriate conditions on the real sequences{αn}and{tn}.

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23

Wang, Ya-qin. "Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings." Journal of Zhejiang University-SCIENCE A 8, no. 10 (2007): 1691–94. http://dx.doi.org/10.1631/jzus.2007.a1691.

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24

Ceng, Lu-Chuan, Q. H. Ansari, and Juei-Ling Ho. "Hybrid Viscosity-like Approximation Methods for General Monotone Variational Inequalities." Taiwanese Journal of Mathematics 15, no. 4 (2011): 1871–96. http://dx.doi.org/10.11650/twjm/1500406385.

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25

Ceng, Lu-Chuan, Hong-Kun Xu, and Ching-Feng Wen. "Relaxed Viscosity Approximation Methods with Regularization for Constrained Minimization Problems." Journal of Applied Mathematics 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/531859.

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We introduce a new relaxed viscosity approximation method with regularization and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a convex minimization problem and a suitable equilibrium problem.

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26

Song, Yisheng, Rudong Chen, and Haiyun Zhou. "Viscosity approximation methods for nonexpansive mapping sequences in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 66, no. 5 (2007): 1016–24. http://dx.doi.org/10.1016/j.na.2006.01.001.

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27

Ceng, Lu-Chuan, and Jen-Chih Yao. "Convergence and certain control conditions for hybrid viscosity approximation methods." Nonlinear Analysis: Theory, Methods & Applications 73, no. 7 (2010): 2078–87. http://dx.doi.org/10.1016/j.na.2010.05.036.

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28

Li, Xue-song, Nan-jing Huang, and Donal O’Regan. "Viscosity approximation methods for pseudo-contractive semigroups in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 75, no. 9 (2012): 3776–86. http://dx.doi.org/10.1016/j.na.2012.01.031.

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29

Chen, Jun-Min, and Tie-Gang Fan. "Viscosity Approximation Methods for Two Accretive Operators in Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/670523.

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We introduced a viscosity iterative scheme for approximating the common zero of two accretive operators in a strictly convex Banach space which has a uniformly Gâteaux differentiable norm. Some strong convergence theorems are proved, which improve and extend the results of Ceng et al. (2009) and some others.

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30

Cockburn, Bernardo. "Continuous dependence and error estimation for viscosity methods." Acta Numerica 12 (May 2003): 127–80. http://dx.doi.org/10.1017/s0962492902000107.

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In this paper, we review some ideas on continuous dependence results for the entropy solution of hyperbolic scalar conservation laws. They lead to a complete L^\infty(L^1)-approximation theory with which error estimates for numerical methods for this type of equation can be obtained. The approach we consider consists in obtaining continuous dependence results for the solutions of parabolic conservation laws and deducing from them the corresponding results for the entropy solution. This is a natural approach, as the entropy solution is nothing but the limit of solutions of parabolic scalar conservation laws as the viscosity coefficient goes to zero.

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31

Pant, Rajendra, Rahul Shukla, and Adrian Petruşel. "Viscosity Approximation Methods for Generalized Multi-Valued Nonexpansive Mappings with Applications." Numerical Functional Analysis and Optimization 39, no. 13 (2018): 1374–406. http://dx.doi.org/10.1080/01630563.2018.1478853.

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32

Ceng, Lu-Chuan, Sy-Ming Guu, and Jen-Chih Yao. "Hybrid viscosity-like approximation methods for nonexpansive mappings in Hilbert spaces." Computers & Mathematics with Applications 58, no. 3 (2009): 605–17. http://dx.doi.org/10.1016/j.camwa.2009.02.035.

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33

Takahashi, Wataru. "Viscosity approximation methods for resolvents of accretive operators in Banach spaces." Journal of Fixed Point Theory and Applications 1, no. 1 (2006): 135–47. http://dx.doi.org/10.1007/s11784-006-0004-3.

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34

Ceng, Lu-Chuan, Qamrul Hasan Ansari, and Jen-Chih Yao. "Viscosity approximation methods for generalized equilibrium problems and fixed point problems." Journal of Global Optimization 43, no. 4 (2008): 487–502. http://dx.doi.org/10.1007/s10898-008-9342-6.

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35

Altwaijry, Najla, Tahani Aldhaban, Souhail Chebbi, and Hong-Kun Xu. "Krasnoselskii–Mann Viscosity Approximation Method for Nonexpansive Mappings." Mathematics 8, no. 7 (2020): 1153. http://dx.doi.org/10.3390/math8071153.

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We show that the viscosity approximation method coupled with the Krasnoselskii–Mann iteration generates a sequence that strongly converges to a fixed point of a given nonexpansive mapping in the setting of uniformly smooth Banach spaces. Our result shows that the geometric property (i.e., uniform smoothness) of the underlying space plays a role in relaxing the conditions on the choice of regularization parameters and step sizes in iterative methods.

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36

Dilshad, Mohammad, Fahad Maqbul Alamrani, Ahmed Alamer, Esmail Alshaban, and Maryam G. Alshehri. "Viscosity-type inertial iterative methods for variational inclusion and fixed point problems." AIMS Mathematics 9, no. 7 (2024): 18553–73. http://dx.doi.org/10.3934/math.2024903.

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<abstract><p>In this paper, we have introduced some viscosity-type inertial iterative methods for solving fixed point and variational inclusion problems in Hilbert spaces. Our methods calculated the viscosity approximation, fixed point iteration, and inertial extrapolation jointly in the starting of every iteration. Assuming some suitable assumptions, we demonstrated the strong convergence theorems without computing the resolvent of the associated monotone operators. We used some numerical examples to illustrate the efficiency of our iterative approaches and compared them with the related work.</p></abstract>

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37

Ghanifard, Azadeh, Hashem Parvaneh Masiha, Manuel De La Sen, and Maryam Ramezani. "Viscosity Approximation Methods for * −Nonexpansive Multi-Valued Mappings in Convex Metric Spaces." Axioms 9, no. 1 (2020): 10. http://dx.doi.org/10.3390/axioms9010010.

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In this paper, we prove convergence theorems for viscosity approximation processes involving * −nonexpansive multi-valued mappings in complete convex metric spaces. We also consider finite and infinite families of such mappings and prove convergence of the proposed iteration schemes to common fixed points of them. Our results improve and extend some corresponding results.

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38

LI, Qiuying, and Sanhua WANG. "Viscosity Approximation Methods for Strong Vector Equilibrium Problems and Fixed Point Problems." Acta Analysis Functionalis Applicata 14, no. 2 (2012): 183. http://dx.doi.org/10.3724/sp.j.1160.2012.00183.

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39

Frimpong, K., and E. Prempeh. "Viscosity Approximation Methods in Reflexive Banach Spaces with a Sequence of Contractions." British Journal of Mathematics & Computer Science 22, no. 3 (2017): 1–10. http://dx.doi.org/10.9734/bjmcs/2017/33414.

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40

Ceng, Lu-Chuan, and Jen-Chih Yao. "Relaxed viscosity approximation methods for fixed point problems and variational inequality problems." Nonlinear Analysis: Theory, Methods & Applications 69, no. 10 (2008): 3299–309. http://dx.doi.org/10.1016/j.na.2007.09.019.

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41

Takahashi, Wataru. "Viscosity approximation methods for countable families of nonexpansive mappings in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 70, no. 2 (2009): 719–34. http://dx.doi.org/10.1016/j.na.2008.01.005.

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42

Zhao, Jing, and Songnian He. "Viscosity Approximation Methods for Split Common Fixed-Point Problem of Directed Operators." Numerical Functional Analysis and Optimization 36, no. 4 (2015): 528–47. http://dx.doi.org/10.1080/01630563.2015.1015079.

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43

Li, Suhong, Yongfu Su, Lingmin Zhang, Huijuan Zhao, and Lihua Li. "Viscosity approximation methods with weak contraction for L-Lipschitzian pseudocontractive self-mapping." Nonlinear Analysis: Theory, Methods & Applications 74, no. 4 (2011): 1031–39. http://dx.doi.org/10.1016/j.na.2010.07.024.

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44

Jeong, Jae Ug. "Generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems." Applied Mathematics and Computation 283 (June 2016): 168–80. http://dx.doi.org/10.1016/j.amc.2015.12.044.

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45

Ceng, Lu-Chuan, Qamrul Hasan Ansari, and Ching-Feng Wen. "Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/854297.

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We first introduce an implicit relaxed method with regularization for finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mappingSin the intermediate sense and the set of solutions of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in the setting of Hilbert spaces. The implicit relaxed method with regularization is based on three well-known methods: the extragradient method, viscosity approximation method, and gradient projection algorithm with regularization. We derive a weak convergence theorem for two sequences generated by this method. On the other hand, we also prove a new strong convergence theorem by an implicit hybrid method with regularization for the MP and the mappingS. The implicit hybrid method with regularization is based on four well-known methods: the CQ method, extragradient method, viscosity approximation method, and gradient projection algorithm with regularization.

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46

Voglhuber-Brunnmaier, Thomas, and Bernhard Jakoby. "Higher-Order Models for Resonant Viscosity and Mass-Density Sensors." Sensors 20, no. 15 (2020): 4279. http://dx.doi.org/10.3390/s20154279.

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Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based on the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork-based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243 mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.

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47

MONNIER, J. "FREE CONVECTION WITH RADIATIVE THERMAL TRANSFER OF GREY BODIES: ANALYSIS AND APPROXIMATION BY FINITE ELEMENT METHODS." Mathematical Models and Methods in Applied Sciences 10, no. 09 (2000): 1383–424. http://dx.doi.org/10.1142/s0218202500000677.

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We study a steady-state free (or mixed) convection model in two- or three-dimensions of space, taking into account radiative thermal transfer of grey bodies separated by a nonparticipating media. The existence of a weak solution is proved and the uniqueness is obtained when the viscosity and thermal conductivity of the fluid are large enough. Then, we discretize the model using classical finite element schemes and prove in detail the existence, uniqueness and the convergence of the discrete solution (when the viscosity and the thermal conductivity are large enough and the step size is small enough).

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48

Xiong, Ting-jian, and Heng-you Lan. "Strong Convergence of New Two-Step Viscosity Iterative Approximation Methods for Set-Valued Nonexpansive Mappings in CAT(0) Spaces." Journal of Function Spaces 2018 (July 2, 2018): 1–8. http://dx.doi.org/10.1155/2018/1280241.

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This paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings in CAT(0) spaces. By means of some properties and characteristic to CAT(0) space and using Cauchy-Schwarz inequality and Xu’s inequality, strong convergence theorems of the new two-step viscosity iterative process for set-valued nonexpansive and contraction operators in complete CAT(0) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature.

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49

De La Rosa, Ángel, Gonzalo Ruiz, Enrique Castillo, and Rodrigo Moreno. "Calculation of Dynamic Viscosity in Concentrated Cementitious Suspensions: Probabilistic Approximation and Bayesian Analysis." Materials 14, no. 8 (2021): 1971. http://dx.doi.org/10.3390/ma14081971.

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We present a new focus for the Krieger–Dougherty equation from a probabilistic point of view. This equation allows the calculation of dynamic viscosity in suspensions of various types, like cement paste and self-compacting mortar/concrete. The physical meaning of the parameters that intervene in the equation (maximum packing fraction of particles and intrinsic viscosity), together with the random nature associated with these systems, make the application of the Bayesian analysis desirable. This analysis permits the transformation of parametric-deterministic models into parametric-probabilistic models, which improves and enriches their results. The initial limitations of the Bayesian methods, due to their complexity, have been overcome by numerical methods (Markov Chain Monte Carlo and Gibbs Sampling) and the development of specific software (OpenBUGS). Here we use it to compute the probability density functions that intervene in the Krieger–Dougherty equation applied to the calculation of viscosity in several cement pastes, self-compacting mortars, and self-compacting concretes. The dynamic viscosity calculations made with the Bayesian distributions are significantly better than those made with the theoretical values.

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50

Tang, Jinfang. "Viscosity Approximation Methods for a Family of Nonexpansive Mappings in CAT(0) Spaces." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/389804.

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The purpose of this paper is using the viscosity approximation method to study the strong convergence problem for a family of nonexpansive mappings in CAT(0) spaces. Under suitable conditions, some strong convergence theorems for the proposed implicit and explicit iterative schemes to converge to a common fixed point of the family of nonexpansive mappings are proved which is also a unique solution of some kind of variational inequalities. The results presented in this paper extend and improve the corresponding results of some others.

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