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Journal articles on the topic 'Asymptotically pseudocontractive mappings in the intermediate sense'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Sahu, D. R., Hong-Kun Xu, and Jen-Chih Yao. "Asymptotically strict pseudocontractive mappings in the intermediate sense." Nonlinear Analysis: Theory, Methods & Applications 70, no. 10 (2009): 3502–11. http://dx.doi.org/10.1016/j.na.2008.07.007.

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2

Qin, Xiaolong, Jong Kyu Kim, and Tianze Wang. "On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense." Abstract and Applied Analysis 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/468716.

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An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.

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3

Zegeye, H., M. Robdera, and B. Choudhary. "Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense." Computers & Mathematics with Applications 62, no. 1 (2011): 326–32. http://dx.doi.org/10.1016/j.camwa.2011.05.013.

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4

Qin, Xiaolong, SunYoung Cho, and JongKyu Kim. "Convergence Theorems on Asymptotically Pseudocontractive Mappings in the Intermediate Sense." Fixed Point Theory and Applications 2010, no. 1 (2010): 186874. http://dx.doi.org/10.1155/2010/186874.

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5

Olaleru, J. "Strong Convergence Theorems for Asymptotically Pseudocontractive Mappings in the Intermediate Sense." British Journal of Mathematics & Computer Science 2, no. 3 (2012): 151–62. http://dx.doi.org/10.9734/bjmcs/2012/1569.

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6

Ceng, Lu-Chuan, and Meijuan Shang. "Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods." Mathematics 7, no. 5 (2019): 424. http://dx.doi.org/10.3390/math7050424.

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Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces.

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7

Zhang, Yunpeng. "Demiclosed principals and convergence theorems for asymptotically pseudocontractive nonself-mappings in intermediate sense." Journal of Nonlinear Sciences and Applications 10, no. 04 (2017): 2229–40. http://dx.doi.org/10.22436/jnsa.010.04.73.

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8

Al-Mazrooei, A. E., A. S. M. Alofi, A. Latif, and J. C. Yao. "Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems." Abstract and Applied Analysis 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/251065.

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We propose two iterative algorithms for finding a common element of the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inclusions for maximal monotone and inverse strong monotone mappings, and the set of common fixed points of infinite nonexpansive mappings and an asymptoticallyκ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions.

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9

Zhao, Jing, and Songnian He. "Weak and Strong Convergence Theorems for Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense." Fixed Point Theory and Applications 2010, no. 1 (2010): 281070. http://dx.doi.org/10.1155/2010/281070.

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10

Ceng, Lu-Chuan, Cheng-Wen Liao, Chin-Tzong Pang, and Ching-Feng Wen. "Convex Minimization with Constraints of Systems of Variational Inequalities, Mixed Equilibrium, Variational Inequality, and Fixed Point Problems." Journal of Applied Mathematics 2014 (2014): 1–28. http://dx.doi.org/10.1155/2014/105928.

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We introduce and analyze one iterative algorithm by hybrid shrinking projection method for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: finitely many generalized mixed equilibrium problems, finitely many variational inequalities, the general system of variational inequalities and the fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable condit

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11

Ceng, Lu-Chuan, Cheng-Wen Liao, Chin-Tzong Pang, Ching-Feng Wen, and Zhao-Rong Kong. "Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria." Abstract and Applied Analysis 2014 (2014): 1–25. http://dx.doi.org/10.1155/2014/513678.

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We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose an

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12

Cho, Sun-Young, Shin-Min Kang, and Xiaolong Qin. "ON THE CONVERGENCE OF HYBRID PROJECTION METHODS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN THE INTERMEDIATE SENSE." Communications of the Korean Mathematical Society 26, no. 3 (2011): 473–82. http://dx.doi.org/10.4134/ckms.2011.26.3.473.

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13

Ceng, Lu-Chuan, Adrian Petruşel, and Jen-Chih Yao. "Iterative Approximation of Fixed Points for Asymptotically Strict Pseudocontractive Type Mappings in the Intermediate Sense." Taiwanese Journal of Mathematics 15, no. 2 (2011): 587–606. http://dx.doi.org/10.11650/twjm/1500406223.

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14

Ceng, Lu-Chuan, Sy-Ming Guu, and Jen-Chih Yao. "Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense." Journal of Global Optimization 60, no. 4 (2013): 617–34. http://dx.doi.org/10.1007/s10898-013-0087-5.

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15

Zegeye, H., and N. Shahzad. "Approximation Analysis for a Common Fixed Point of Finite Family of Mappings Which Are Asymptoticallyk-Strict Pseudocontractive in the Intermediate Sense." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/821737.

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We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous asymptoticallyki-strict pseudocontractive mappings in the intermediate sense fori=1,2,…,N. The projection ofx0onto the intersection of closed convex setsCnandQnfor eachn≥1is not required. Moreover, the restriction that the interior of common fixed points is nonempty is not required. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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16

Ceng, Lu-Chuan, and Juei-Ling Ho. "Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems." Abstract and Applied Analysis 2014 (2014): 1–27. http://dx.doi.org/10.1155/2014/436069.

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We introduce two iterative algorithms by the hybrid extragradient method with regularization for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inequalities for inverse strong monotone mappings and the set of fixed points of an asymptoticallyκ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the prop

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17

Tianchai, Pattanapong. "Shrinking Projection Method of Fixed Point Problems for Asymptotically Pseudocontractive Mapping in the Intermediate Sense and Mixed Equilibrium Problems in Hilbert Spaces." Journal of Applied Mathematics 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/187421.

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This paper is concerned with a common element of the set of fixed point for an asymptotically pseudocontractive mapping in the intermediate sense and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method, which extends and improves that of Qin et al. (2010) and many others.

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18

Qin, Xiaolong, Jong Kyu Kim, and Tianze Wang. "Erratum to “On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense”." Abstract and Applied Analysis 2012 (2012): 1. http://dx.doi.org/10.1155/2012/265945.

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19

Ge, Ci-Shui. "A hybrid algorithm with variable coefficients for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains." Nonlinear Analysis: Theory, Methods & Applications 75, no. 5 (2012): 2859–66. http://dx.doi.org/10.1016/j.na.2011.11.026.

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20

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 tw

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21

Ceng, Lu-Chuan, and Jen-Chih Yao. "Strong Convergence Theorems for Variational Inequalities and Fixed Point Problems of Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense." Acta Applicandae Mathematicae 115, no. 2 (2011): 167–91. http://dx.doi.org/10.1007/s10440-011-9614-x.

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22

Ceng, Lu-Chuan, Cheng-Wen Liao, Chin-Tzong Pang, and Ching-Feng Wen. "Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems." Abstract and Applied Analysis 2014 (2014): 1–27. http://dx.doi.org/10.1155/2014/637324.

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We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. O

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23

Hu, Chang song, and Gang Cai. "Convergence theorems for equilibrium problems and fixed point problems of a finite family of asymptotically k-strictly pseudocontractive mappings in the intermediate sense." Computers & Mathematics with Applications 61, no. 1 (2011): 79–93. http://dx.doi.org/10.1016/j.camwa.2010.10.034.

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24

Qin, Xiaolong, та Lin Wang. "On Asymptotically Quasi-ϕ-Nonexpansive Mappings in the Intermediate Sense". Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/636217.

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A projection iterative process is investigated for the class of asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common fixed points of a family of asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense are established in the framework of Banach spaces.

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25

Verma, Anurag, and B. P. Tripathi. "Approximation of common fixed point of two asymptotically nonexpansive mappings in the intermediate sense for a new iteration process in CAT(0) spaces." Annals of Mathematics and Computer Science 24 (June 23, 2024): 85–98. http://dx.doi.org/10.56947/amcs.v24.341.

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In this paper, we establish strong and ∆−convergence for a new iteration process containing two asymptotically nonexpansive mappings in the intermediate sense which is broader than the class of asymptotically nonexpansive mappings in the context of CAT(0) spaces. Our results extend, generalize, and improve many well-known results in the literature.

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26

Saluja, Gurucharan Singh. "Strong Convergence Theorems for Hybrid Mixed Type Nonlinear Mappings in Banach Spaces." Annals of West University of Timisoara - Mathematics and Computer Science 56, no. 1 (2018): 136–48. http://dx.doi.org/10.2478/awutm-2018-0009.

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Abstract In this paper, we introduce a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some strong convergence theorems for mentioned scheme and mappings in Banach spaces. Our results extend and generalize the corresponding results recently announced by Wei and Guo [16] (Comm. Math. Res. 31(2015), 149-160) and many others.

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27

Okeke, G. "Convergence Theorems on Generalized Strongly Successively -pseudocontractive Mappings in the Intermediate Sense." British Journal of Mathematics & Computer Science 3, no. 3 (2013): 415–24. http://dx.doi.org/10.9734/bjmcs/2013/2430.

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28

Oka, Hirokazu. "An ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense." Proceedings of the American Mathematical Society 125, no. 6 (1997): 1693–703. http://dx.doi.org/10.1090/s0002-9939-97-03745-3.

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29

Li, Liuhong, and Yuanheng Wang. "Strong Convergence of a Modified Ishikawa Iterative Sequence for Asymptotically Quasi-Pseudo-Contractive-Type Mappings." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/981494.

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The purpose of this paper is to investigate the strong convergence problem of a modified mixed Ishikawa iterative sequence with errors for approximating the fixed points of an asymptotically nonexpansive mapping in the intermediate sense and an asymptotically quasi-pseudo-contractive-type mapping in an arbitrary real Banach space. The results here improve and extend the corresponding results reported by some other authors recently.

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30

Saluja, Gurucharan S., Mihai Postolache, and Adrian Ghiura. "Convergence theorems for mixed type asymptotically nonexpansive mappings in the intermediate sense." Journal of Nonlinear Sciences and Applications 09, no. 07 (2016): 5119–35. http://dx.doi.org/10.22436/jnsa.009.07.14.

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31

Chidume, C. E., Naseer Shahzad#, and Habtu Zegeye#. "Convergence Theorems for Mappings Which Are Asymptotically Nonexpansive in the Intermediate Sense." Numerical Functional Analysis and Optimization 25, no. 3-4 (2005): 239–57. http://dx.doi.org/10.1081/nfa-120039611.

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32

Okeke, G. A., J. O. Olaleru, and H. Akewe. "Convergence theorems on asymptotically generalized \Phi-hemicontractive mappings in the intermediate sense." International Journal of Mathematical Analysis 7 (2013): 1991–2003. http://dx.doi.org/10.12988/ijma.2013.35117.

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33

Huang, Jui-Chi. "On Common Fixed Points of Asymptotically Nonexpansive Mappings in the Intermediate Sense." Czechoslovak Mathematical Journal 54, no. 4 (2004): 1055–63. http://dx.doi.org/10.1007/s10587-004-6450-4.

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34

Ceng, L. C., D. R. Sahu, and J. C. Yao. "Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings." Journal of Computational and Applied Mathematics 233, no. 11 (2010): 2902–15. http://dx.doi.org/10.1016/j.cam.2009.11.035.

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35

Tomizawa, Yukino. "Asymptotically quasi-nonexpansive mappings with respect to the Bregman distance in the intermediate sense." Fixed Point Theory 18, no. 1 (2017): 391–406. http://dx.doi.org/10.24193/fpt-ro.2017.1.31.

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36

Oke, A., and D. Kayode. "Some Theorems on Fixed Points Set of Asymptotically Demicontractive Mappings in the Intermediate Sense." Asian Research Journal of Mathematics 6, no. 4 (2017): 1–7. http://dx.doi.org/10.9734/arjom/2017/36218.

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37

Abbas, Mujahid, Balwant Singh Thakur, and Dipti Thakur. "FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE IN CAT(0) SPACES." Communications of the Korean Mathematical Society 28, no. 1 (2013): 107–21. http://dx.doi.org/10.4134/ckms.2013.28.1.107.

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38

Okeke, G. A., J. O. Olaleru, and H. Akewe. "Existence of fixed points of asymptotically generalized \Phi-hemicontractive mappings in the intermediate sense." Applied Mathematical Sciences 7 (2013): 4891–98. http://dx.doi.org/10.12988/ams.2013.36338.

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39

Kaczor, Wiesława, Tadeusz Kuczumow, and Simeon Reich. "A mean ergodic theorem for mappings which are asymptotically nonexpansive in the intermediate sense." Nonlinear Analysis: Theory, Methods & Applications 47, no. 4 (2001): 2731–42. http://dx.doi.org/10.1016/s0362-546x(01)00392-3.

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40

罗, 秋瑾. "Common Fixed Points Approximation Algorithm for Asymptotically Quasi-?-Nonexpansive Mappings in the Intermediate Sense." Pure Mathematics 13, no. 11 (2023): 3316–24. http://dx.doi.org/10.12677/pm.2023.1311344.

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41

WIŚNICKI, ANDRZEJ. "THE FIXED POINT PROPERTY IN DIRECT SUMS AND MODULUS." Bulletin of the Australian Mathematical Society 89, no. 1 (2013): 79–91. http://dx.doi.org/10.1017/s0004972713000440.

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AbstractWe show that the direct sum $\mathop{({X}_{1} \oplus \cdots \oplus {X}_{r} )}\nolimits_{\psi } $ with a strictly monotone norm has the weak fixed point property for nonexpansive mappings whenever $M({X}_{i} )\gt 1$ for each $i= 1, \ldots , r$. In particular, $\mathop{({X}_{1} \oplus \cdots \oplus {X}_{r} )}\nolimits_{\psi } $ enjoys the fixed point property if Banach spaces ${X}_{i} $ are uniformly nonsquare. This combined with the earlier results gives a definitive answer for $r= 2$: a direct sum ${X}_{1} {\mathop{\oplus }\nolimits}_{\psi } {X}_{2} $ of uniformly nonsquare spaces with

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42

Ma, Zhaoli, and Yunhe Zhao. "The split common fixed point problem for asymptotically quasi-nonexpansive mappings in the intermediate sense." International Mathematical Forum 8 (2013): 1233–41. http://dx.doi.org/10.12988/imf.2013.3599.

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43

Liang, Hongwei, and Mingliang Zhang. "Some results on asymptotically quasi-phi-nonexpansive mappings in the intermediate sense and Ky Fan inequalities." Journal of Nonlinear Sciences and Applications 09, no. 04 (2016): 1675–84. http://dx.doi.org/10.22436/jnsa.009.04.23.

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44

Ma, Zhaoli, Lin Wang та Shih-sen Chang. "Strong convergence theorem for quasi-ϕ-asymptotically nonexpansive mappings in the intermediate sense in Banach spaces". Journal of Inequalities and Applications 2013, № 1 (2013): 306. http://dx.doi.org/10.1186/1029-242x-2013-306.

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45

Saluja, G. S. "Convergence theorems of finite-step iteration with errors for non-self asymptotically nonexpansive in the intermediate sense mappings." Filomat 25, no. 1 (2011): 81–103. http://dx.doi.org/10.2298/fil1101081s.

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Let K be a nonempty closed convex nonexpansive retract of a uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K ? E be non-self asymptotically nonexpansive in the intermediate sense mapping with F(T) = ?. Let {?ni}, {?ni} and {?ni} are sequences in [0, 1] with ?n(i) + ?n(i) + ?n(i) = 1 for all i = 1, 2, . . . , N. From arbitrary x1 ? K , define the sequence {xn } iteratively by (8), where {u(i) } for all i = 1, 2, . . . , N are bounded sequences in K with P? u(i) < ?. (i) If the dual E

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46

Banerjee, Shrabani, and Binayak Samadder Choudhury. "WEAK AND STRONG CONVERGENCE CRITERIA OF MODIFIED NOOR ITERATIONS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE." Bulletin of the Korean Mathematical Society 44, no. 3 (2007): 493–506. http://dx.doi.org/10.4134/bkms.2007.44.3.493.

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47

Jeong, Jae Ug. "STRONG CONVERGENCE THEOREMS FOR FIXED POINT PROBLEMS OF ASYMPTOTICALLY QUASI-𝜙-NONEXPANSIVE MAPPINGS IN THE INTERMEDIATE SENSE". Journal of applied mathematics & informatics 32, № 5_6 (2014): 621–33. http://dx.doi.org/10.14317/jami.2014.621.

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48

Lin, Lai-Jiu, Zenn-Tsun Yu, and Chih-Sheng Chuang. "Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces." Journal of Global Optimization 56, no. 1 (2012): 165–83. http://dx.doi.org/10.1007/s10898-012-9968-2.

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49

Ansari, Qamrul Hasan, Aisha Rehan, and Jen-Chih Yao. "Split feasibility and fixed point problems for asymptotically k-strict pseudo-contractive mappings in intermediate sense." Fixed Point Theory 18, no. 1 (2017): 57–68. http://dx.doi.org/10.24193/fpt-ro.2017.1.06.

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50

Saluja, Singh. "Convergence to common fixed point for two asymptotically quasi-nonexpansive mappings in the intermediate sense in Banach spaces." Mathematica Moravica 19, no. 2 (2015): 33–48. http://dx.doi.org/10.5937/matmor1501033s.

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