Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces

We introduce a new hybrid iterative scheme for finding a common element in the solutions set of a system of equilibrium problems and the common fixed points set of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We prove the strong convergence theorem by the shrinking projection method. In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space

A Projection Method for Relatively Nonexpansive Mappings in Banach Spaces

Abstract We introduce a new projection algorithm for solving the fixed point problem of relatively nonexpansive mappings in the framework of Banach spaces. We also prove the strong convergence theorem for such mappings. Mathematics Subject Classification: 47H09, 47H1

Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems

We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems

Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications

We introduce a Halpern-type iteration for a generalized mixed equilibrium problem in uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are also established in this paper. As applications, we apply our main result to mixed equilibrium, generalized equilibrium, and mixed variational inequality problems in Banach spaces. Finally, examples and numerical results are also given

Convergence theorems for finding the split common null point in Banach spaces

[EN] In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.S. Suantai wish to thank Chiang Mai University for financial supports. P. Cholamjiak was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248.Suantai, S.; Srisap, K.; Naprang, N.; Mamat, M.; Yundon, V.; Cholamjiak, P. (2017). Convergence theorems for finding the split common null point in Banach spaces. Applied General Topology. 18(2):345-360. https://doi.org/10.4995/agt.2017.725734536018

A Hybrid Iterative Scheme for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Banach Spaces

<p/> <p>The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.</p

On Ishikawa-Type Iteration with Errors for a Continuous Real Function on an Arbitrary Interval

Abstract We consider the Ishikawa-type iteration process with errors for a continuous real function on an arbitrary interval and prove the convergence theorem. Furthermore, we give numerical examples to compare with Mann and Ishikawa iteration processes with error sequences. Mathematics Subject Classification: 47H09, 47H1

Convergence Theorems for Generalized Equilibrium Problems and Nonexpansive Mappings

Abstract We propose a general iterative scheme for solving a generalized equilibrium problem and fixed points of nonexpansive mappings in a Hilbert space. We then prove strong convergence theorems. Mathematics Subject Classification: 47H09, 47H1

Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces.

Tyt. z nagłówka.Bibliogr. s. 77-79.We prove the strong convergence of the modified Mann-type iterative scheme for a countable family of strict pseudocontractions in q-uniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y. Yao, H. Zhou, Y.-C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J. Appl. Math. Comput. 29 (2009), 383–389].Dostępny również w formie drukowanej.KEYWORDS: common fixed points, convergence theorem, modified Mann iteration, strict pseudocontractions, q-uniformly smooth Banach spaces