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Journal articles on the topic 'Asymptotically strict 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

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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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

Guo, Yan-Ni, Qiao-Li Dong, and Zhi-Fei Zhang. "Notes on weak and strong convergence theorems for a finite family of asymptotically strict pseudo-contractive mappings in the intermediate sense." Computers & Mathematics with Applications 62, no. 4 (2011): 2132–41. http://dx.doi.org/10.1016/j.camwa.2011.06.021.

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25

Olaleru, J. O., and G. A. Okeke. "Strong Convergence Theorems for Asymptotically Pseudocontractive Mappings in the Intermediate Sense." October 13, 2012. https://doi.org/10.5281/zenodo.9022.

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In this study, we prove a strong convergence of Noor type scheme for a uniformly L-Lipschitzian and asymptotically pseudocontractive mappings in the intermediate sense without assuming any form of compactness. Consequently, we also obtain a convergence result for the class of asymptotically strict pseudocontractive mappings in the intermediate sense. Our results are improvements and extensions of some of the results in literature.

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26

Ge, Ci-Shui. "Strong convergence of iterative algorithms with variable coefficients for asymptotically strict pseudocontractive mappings in the intermediate sense and monotone mappings." Fixed Point Theory and Applications 2012, no. 1 (2012). http://dx.doi.org/10.1186/1687-1812-2012-68.

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27

Tianchai, Pattanapong. "An approximate solution to the fixed point problems for an infinite family of asymptotically strictly pseudocontractive mappings in the intermediate sense, cocoercive quasivariational inclusions problems and mixed equilibrium problems in Hilbert spaces." Fixed Point Theory and Applications 2012, no. 1 (2012). http://dx.doi.org/10.1186/1687-1812-2012-214.

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