Approximation Solvability of a Class of A-monotone Variational Inclusion Problems in Semi-inner Product Spaces

Implicit Variational Inclusions and Algorithms Involving (A, η)-monotone Operators in 2-uniformly Smooth Banach Spaces

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is inve...

System of nonlinear variational inclusion problems with (A, η)-maximal monotonicity in Banach spaces

This paper deals with a new system of nonlinear variational inclusion problems involving (A, η)-maximal relaxed monotone and relative (A, η)-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of t...

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

Research Article Generalized Nonlinear Variational Inclusions Involving (A,)-Monotone Mappings in Hilbert Spaces

A new class of generalized nonlinear variational inclusions involving (A,η)-monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since (A,η)monotonicity generalizes A-monotonicity and H-monotonic...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems