A modified contraction method for solving certain class of split monotone variational inclusion problems with application

2020 ◽  
Vol 39 (3) ◽  
Author(s):  
C. Izuchukwu ◽  
J. N. Ezeora ◽  
J. Martinez-Moreno
Keyword(s):  
Variational Inclusion ◽  
Inclusion Problems ◽  
Contraction Method

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.

A new proximal-like algorithm for solving split variational inclusion problems

2021 ◽  
Author(s):  
Dang Van Hieu ◽  
Simeon Reich ◽  
Pham Ky Anh ◽  
Nguyen Hai Ha
Keyword(s):  
Variational Inclusion ◽  
Inclusion Problems

scholarly journals Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 123 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Iterative Method ◽  
Hilbert Spaces ◽  
Optimization Problem ◽  
Variational Inclusion ◽  
Hierarchical Optimization ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem ◽  
General Iterative Method

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions.

scholarly journals A-monotonicity and applications to nonlinear variational inclusion problems

2004 ◽  
Vol 2004 (2) ◽  
pp. 193-195 ◽  
Author(s):  
Ram U. Verma
Keyword(s):  
Existence Of Solutions ◽  
Variational Inclusion ◽  
Hemivariational Inequalities ◽  
Energy Functions ◽  
Inclusion Problems ◽  
Constrained Problems ◽  
Nonconvex Energy

A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity. Since the A-monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.

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