scholarly journals CONTRACTION-MAPPING ALGORITHM FOR THE EQUILIBRIUM PROBLEM OVER THE FIXED POINT SET OF A NONEXPANSIVE SEMIGROUP

2018 ◽  
Vol 24 (1) ◽  
pp. 43-61
Author(s):  
Trinh Ngoc Hai ◽  
Le Qung Thuy
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Nonexpansive Semigroup ◽  
Strong Monotonicity ◽  
Fixed Point Set ◽  
Proximal Mapping ◽  
Mapping Algorithm ◽  
Point Set ◽  
Monotonicity Conditions ◽  
Weak Convergence Theorem

In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented.

scholarly journals Approximation of a Common Element of the Fixed Point Sets of Multivalued Strictly Pseudocontractive-Type Mappings and the Set of Solutions of an Equilibrium Problem in Hilbert Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
F. O. Isiogugu
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Contemporary Literature ◽  
Common Element ◽  
Point Sets ◽  
Fixed Point Set ◽  
Strict Fixed Point ◽  
Point Set ◽  
Fixed Point Sets

The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature.

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Qamrul Hasan Ansari ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Hybrid Extragradient Method ◽  
Point Set ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

Stein manifolds of nonnegative curvature

2018 ◽  
Vol 18 (3) ◽  
pp. 285-287
Author(s):  
Xiaoyang Chen
Keyword(s):  
Fixed Point ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Stein Manifold ◽  
Riemannian Metric ◽  
Nonnegative Curvature ◽  
Fixed Point Set ◽  
Nonnegative Sectional Curvature ◽  
Point Set ◽  
Nonempty Compact

AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

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