scholarly journals The existence of solution for equilibrium problems in Hadamard manifolds

2017 ◽  
Vol 171 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Salahuddin
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solution ◽  
Hadamard Manifolds

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals On Mixed Equilibrium Problems in Hadamard Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chinedu Izuchukwu ◽  
Kazeem Olalekan Aremu ◽  
Olawale Kazeem Oyewole ◽  
Oluwatosin Temitope Mewomo ◽  
Safeer Hussain Khan
Keyword(s):  
Equilibrium Problem ◽  
Resolvent Operator ◽  
Equilibrium Problems ◽  
Existence Of Solution ◽  
Mixed Equilibrium Problem ◽  
Proximal Point ◽  
Unique Existence ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
The Resolvent Operator

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

scholarly journals Existence Results for Some Equilibrium Problems Involvingα-Monotone Bifunction

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Ayed E. Hashoosh ◽  
Mohsen Alimohammady ◽  
M. K. Kalleji
Keyword(s):  
Banach Spaces ◽  
Differential Inclusion ◽  
Equilibrium Problems ◽  
Existence Of Solution ◽  
Existence Results ◽  
Closed Sets ◽  
Monotone Bifunction

This paper deals with some existence results of equilibrium problems(EPΨ)on convex and closed sets (either bounded or unbounded) in Banach spaces. Moreover, an application to the existence of solution for a differential inclusion is given.

scholarly journals Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds

2021 ◽  
Vol 37 (3) ◽  
pp. 393-406
Author(s):  
SULIMAN AL-HOMIDAN ◽  
◽  
QAMRUL HASAN ANSARI ◽  
MONIRUL ISLAM ◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Coercivity Conditions ◽  
Hadamard Manifolds ◽  
Type Condition ◽  
Proximal Point ◽  
Strong Pseudomonotonicity

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

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