An Inertial Iterative Algorithm to Find Common Solution of a Split Generalized Equilibrium and a Variational Inequality Problem in Hilbert Spaces

Abstract

In this paper, we introduce and study an iterative algorithm via inertial and viscosity techniques to find a common solution of a split generalized equilibrium and a variational inequality problem in Hilbert spaces. Further, we prove that the sequence generated by the proposed theorem converges strongly to the common solution of our problem. Furthermore, we list some consequences of our established algorithm. Finally, we construct a numerical example to demonstrate the applicability of the theorem. We emphasize that the result accounted in the manuscript unifies and extends various results in this field of study.

Solving System of Mixed Ordered Variational Inequalities Involving XOR and XNOR Operations in Ordered Product Banach Space

“…In 1972, Amann [1] established for computing the solutions of nonlinear equations and fixed point theory with nonlinear mapping and applications have been studied with nonlinear increasing operators in real ordered Hilbert space or Banach spaces investigated by Du [18] which is applicable in nonlinear analysis and developed the methods to solve original mathematical problems. Future, many authors discussed and studied the idea of ordered nonlinear variational inequalities (inclusions) in different settings which is available in the literature [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

On Split Generalized Equilibrium and Fixed Point Problems of Bregman W-Mappings With Multiple Output Sets in Reflexive Banach Spaces

“…The Equilibrium Problem is known to include many mathematical problems, for example, variational inclusion problem, complementary problem, saddle point problem, Nash equilibrium problem in non-cooperative games, minimax inequality problem, minimization problem, variational inequality problem and fixed point problem, see [6,11,14,17,19,22,33,34,37]. Let D and E be nonempty, closed and convex subsets of two real Banach spaces Y 1 and Y 2 respectively.…”

New Convergence Theorems for Pseudomonotone Variational Inequality on Hadamard Manifolds

“…The main advantages of these extensions are that non-convex problems and constrained problems in spaces with linear structure and symmetry may be transformed into convex problems and unconstrained problems on Hadamard manifolds without linear structure, respectively. So, many nonlinear problems on symmetric Hadamard manifolds have been attracted and studied by some authors, see for example [19][20][21][22][23][24][25][26][27][28][29] and the reference therein.…”