scholarly journals Generalized Complementarity Problem with Three Classes of Generalized Variational Inequalities Involving ⊕ Operation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rais Ahmad ◽  
Iqbal Ahmad ◽  
Zahoor Ahmad Rather ◽  
Yuanheng Wang
Keyword(s):  
Variational Inequalities ◽  
Iterative Algorithm ◽  
Complementarity Problem ◽  
Convergence Result ◽  
Generalized Variational Inequalities ◽  
Generalized Complementarity Problem ◽  
Xor Operation

In this study, we introduce and study a generalized complementarity problem involving XOR operation and three classes of generalized variational inequalities involving XOR operation. Under certain appropriate conditions, we establish equivalence between them. An iterative algorithm is defined for solving one of the three generalized variational inequalities involving XOR operation. Finally, an existence and convergence result is proved, supported by an example.

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

scholarly journals On the generalized complementarity problem

1994 ◽  
Vol 35 (4) ◽  
pp. 420-428 ◽  
Author(s):  
Jen-Chih Yao
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problem ◽  
Existence Results ◽  
Generalized Complementarity Problem ◽  
Extended Problem

AbstractIn this paper, the generalised complementarity problem studied by Parida and Sen [13] is further extended. The extended problem appears to be more general and unifying. Characterisations of solutions to this extended problem are given. Some existence results derived by these characterisations are presented. An application of the extended problem to the quasi-variational inequalities of obstacle type is considered.

scholarly journals System of Multi-Valued Mixed Variational Inclusions with XOR-Operation in Real Ordered Uniformly Smooth Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1027
Author(s):  
Rais Ahmad ◽  
Imran Ali ◽  
Xiao-Bing Li ◽  
Mohd. Ishtyak ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Variational Inclusions ◽  
Uniformly Smooth ◽  
Xor Operation ◽  
Uniformly Smooth Banach Spaces

In this paper, we consider and study a system of multi-valued mixed variational inclusions with XOR-operation ⊕ in real ordered uniformly smooth Banach spaces. This system consists of bimappings, multi-valued mappings and Cayley operators. An iterative algorithm is suggested to find the solution to a system of multi-valued mixed variational inclusions with XOR-operation ⊕ and consequently an existence and convergence result is proved. In support of our main result, an example is constructed.

scholarly journals Unique solvability of weakly homogeneous generalized variational inequalities

2021 ◽  
Author(s):  
Xueli Bai ◽  
Mengmeng Zheng ◽  
Zheng-Hai Huang
Keyword(s):  
Variational Inequalities ◽  
Unique Solvability ◽  
Generalized Variational Inequalities

scholarly journals Iterative Computation for Solving the Variational Inequality and the Generalized Equilibrium Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xiujuan Pan ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Generalized Equilibrium Problem ◽  
Iterative Computation ◽  
Generalized Equilibrium

An iterative algorithm for solving the variational inequality and the generalized equilibrium problem has been introduced. Convergence result is given.

scholarly journals An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1915
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Line Search ◽  
Convex Combination ◽  
Extragradient Method ◽  
Convergence Result ◽  
Armijo Line Search ◽  
Systems Of Variational Inequalities ◽  
Demicontractive Mappings ◽  
The Cost

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method.

Generalized variational inequalities and minimax theorems

1991 ◽  
Vol 12 (9) ◽  
pp. 863-869
Author(s):  
Yan Xin-li ◽  
Li Bing-you
Keyword(s):  
Variational Inequalities ◽  
Minimax Theorems ◽  
Generalized Variational Inequalities
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