The subgradient extragradient method for approximation of fixed-point problem and modification of equilibrium problem

Optimization ◽  
2021 ◽  
pp. 1-28
Author(s):  
Kanyanee Saechou ◽  
Atid Kangtunyakarn
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Subgradient Extragradient Method

scholarly journals A Parallel Hybrid Bregman Subgradient Extragradient Method for a System of Pseudomonotone Equilibrium and Fixed Point Problems

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 216
Author(s):  
Annel Thembinkosi Bokodisa ◽  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Convergence Result ◽  
Point Problem ◽  
Subgradient Extragradient Method ◽  
Reflexive Banach Spaces ◽  
Common Fixed Point Problem ◽  
Parallel Hybrid

We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.

scholarly journals Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Pongrus Phuangphoo ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Dual Space ◽  
Fixed Point Problem ◽  
Generalized Mixed Equilibrium Problem ◽  
Point Problem ◽  
Mixed Equilibrium Problem ◽  
Existence Of A Solution ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We study and establish the existence of a solution for a generalized mixed equilibrium problem with a bifunction defined on the dual space of a Banach space. Furthermore, we also modify Halpern-Mann iterations for finding a common solution of a generalized mixed equilibrium problem and a fixed point problem. Under suitable conditions of the purposed iterative sequences, the strong convergence theorems are established by using sunny generalized nonexpansive retraction in Banach spaces. Our results extend and improve various results existing in the current literature.

scholarly journals Split equality common null point problem for Bregman quasi-nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3917-3932
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Optimization Problem ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Fixed Point Problem ◽  
Null Point ◽  
Point Problem ◽  
Reflexive Banach Spaces

In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].

scholarly journals On strong convergence theorems for a viscosity-type extragradient method

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 1033-1043
Author(s):  
L.C. Ceng ◽  
C.S. Fong
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Monotone Mapping ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Inclusion Problem ◽  
Point Problem ◽  
Asymptotically Nonexpansive

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and the variational inclusion problem with two accretive operators. We obtain a strong convergence theorem in the setting of Banach spaces. In terms of this theorem, we establish the strong convergence result for solving the fixed point problem (FPP) of an asymptotically nonexpansive mapping and the variational inequality problem (VIP) for an inverse-strongly monotone mapping in the framework of Hilbert spaces. Finally, this result is applied to deal with the VIP and FPP in an illustrating example.

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