STRONG AND WEAK CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND RELATIVELY NONEXPANSIVE MAPPINGS IN BANACH SPACES

By Wataru Takahashi, K. Zembayashi. 2009

366 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/bb1f2bf84eec756959cc799c6bfac80b0a4a956e

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Citations in the corpus

Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-ϕ-nonexpansive mappings (2011, background): “(b): (Refs. [25, 33 ]) Define a mapping Tr : E ® Cb y”
A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces (2010, methodology): “The results obtained in this paper improve and extend the recent ones announced by Takahashi and Zembayashi [20], Wattanawitoon and Kumam [25], Plubtieng and Ungchittrakool [41] and many others.”
Strong convergence theorem for a common point of solution of variational inequality and fixed point problem (2012, neutral): “Recently, many authors have considered the problem of ﬁnding a common element of the ﬁxed points set of relatively nonexpansive mapping and the solution set of variational inequality problem for γ − inverse monotone mapping (see, e.g., [8, 13, 15, 17, 20, 21]).”
Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems (2015, background): “element in F (T ) ⋂ EP (f), Takahashi and Zembayashi [20] introduced the following algorithm in a uniformly smooth and uniformly convex Banach space:    x0 ∈ C, yn = J (αnJxn + (1− αn)JTyn), un ∈ C, such that, f(un, y) + 1 rn 〈y − un, Jun − Jyn〉 ≥ 0 ∀y ∈ C, Hn = {v ∈ C : φ(v, un) ≤ φ(v,”
Generalized mixed equilibrium problem in Banach spaces (2009, background): “Recently, many authors studied the problems of finding a common element of the set of fixed points for a nonexpansive mapping and the set of solutions to an equilibrium problem in the setting of Hilbert space and uniformly smooth and uniformly convex Banach space, respectively (see, for instance, [ ”
Generalized mixed equilibrium and fixed point problems in a Banach space (2016, background): “Recently, the above nonlinear problems have been extensively studied based on iterative techniques; see [3], [6]-[10], [14]–[17], [19], [22]-[26] and the references therein.”