Absolute Value Variational Inclusions

In this paper, we consider a new system of absolute value variational inclusions. Some interesting and extensively problems such as absolute value equations, difference of monotone operators, absolute value complementarity problem and hemivariational inequalities as special case. It is shown that variational inclusions are equivalent to the fixed point problems. This alternative formulation is used to study the existence of a solution of the system of absolute value inclusions. New iterative methods are suggested and investigated using the resolvent equations, dynamical system and nonexpansive mappings techniques. Convergence analysis of these methods is investigated under monotonicity. Some special cases are discussed as applications of the main results.

Strong convergence algorithm for the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem

The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.

Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators

Iterative methods for solving variational inclusions and fixed-point problems have been considered and investigated by many scholars. In this paper, we use the Halpern-type method for finding a common solution of variational inclusions and fixed-point problems of pseudocontractive operators. We show that the proposed algorithm has strong convergence under some mild conditions.