A new algorithm for finding a common solution of a split variational inequality problem, the fixed point problems and the variational inclusion problems

In this paper, a cyclic algorithm for approximating a class of split variational inequality problem is introduced and studied in some Banach spaces. A strong convergence theorem is proved. Some applications of the theorem are presented. The results presented here improve, unify, and generalize certain recent results in the literature.

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An iterative scheme for split monotone variational inclusion, variational inequality and fixed point problems

Advances in Difference Equations ◽

10.1186/s13662-020-02942-0 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Monairah Alansari ◽

Mohammad Farid ◽

Rehan Ali

Keyword(s):

Fixed Point ◽

Variational Inequality ◽

Hilbert Spaces ◽

Iterative Scheme ◽

Nonexpansive Mappings ◽

Infinite Family ◽

Fixed Point Problems ◽

Variational Inclusion ◽

Common Solution ◽

New Type

Abstract We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established theorem. Finally, we provide a numerical example to demonstrate the applicability of the algorithm. We emphasize that the result accounted in manuscript unifies and extends various results in this field of study.

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Algorithms for the Split Variational Inequality Problem

Numerical Algorithms ◽

10.1007/s11075-011-9490-5 ◽

2011 ◽

Vol 59 (2) ◽

pp. 301-323 ◽

Cited By ~ 240

Author(s):

Yair Censor ◽

Aviv Gibali ◽

Simeon Reich

Keyword(s):

Variational Inequality ◽

Variational Inequality Problem ◽

Inequality Problem ◽

Split Variational Inequality ◽

Split Variational Inequality Problem

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Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem

Advances in Pure and Applied Mathematics ◽

10.1515/apam-2017-0132 ◽

2019 ◽

Vol 10 (4) ◽

pp. 339-353 ◽

Cited By ~ 2

Author(s):

Ferdinard U. Ogbuisi ◽

Oluwatosin T. Mewomo

Keyword(s):

Variational Inequality ◽

Variational Inequality Problem ◽

Iterative Scheme ◽

Real Hilbert Space ◽

Operator Norm ◽

Step Size ◽

Inequality Problem ◽

Convex Minimization Problems ◽

Split Variational Inequality ◽

Split Variational Inequality Problem

AbstractIn this paper, we introduce an iterative scheme involving an inertial term and a step size independent of the operator norm for approximating a solution to a split variational inequality problem in a real Hilbert space. Furthermore, we prove a convergence theorem for the sequence generated by the proposed operator norm independent inertial accelerated iterative scheme. We applied our result to solve split convex minimization problems, split zero problem and further give a numerical example to demonstrate the efficiency of the proposed algorithm.

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