In this paper, we propose a SPLIT nonCONVEX VARIATIONAL INEQUALITY PROBLEM which is a natural extension of SPLIT CONVEX VARIATIONAL INEQUALITY PROBLEM in two different Hilbert spaces. Relying on the prox-regularity notion, we introduce and establish the convergence of an iterative method for the new SPLIT nonCONVEX VARIATIONAL INEQUALITY PROBLEM. Further, we also establish the convergence of an iterative method for the SPLIT CONVEX VARIATIONAL INEQUALITY PROBLEM. The results presented in this paper are new and different form the previously known results for nonCONVEX (CONVEX) VARIATIONAL INEQUALITY PROBLEMs. These results also generalize, unify, and improve the previously known results of this area.

In this paper, we introduce a new iterative algorithm of inertial form for approximating the solution of SPLIT VARIATIONAL Inclusion PROBLEM (SVIP) involving accrective operators in Banach space. Mo-tivated by the inertial technique, we incorporate the inertial term to accelerate the convergence of the proposed method. Under standard and mild assumption of monotonicity of the SVIP associated mappings, we establish the weak convergence of the sequence generated by our algorithm. Some applications and numerical example are presented to illustrate the performance of our method as well as comparing it with the non-inertial version.

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.

In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of SPLIT equilibrium PROBLEMs and the set of common solutions of a finite family of VARIATIONAL INEQUALITY PROBLEMs in real Hilbert spaces. Moreover, the sequence generated by the proposed algorithm is proved to be strongly convergent to a common solution of these three PROBLEMs under mild conditions on parameters. Our results improve and generalize many well-known recent results existing in the literature in this field of research.

In this paper, we introduce a new type of modified generalized α,-nonexpansive mapping and establish some fixed point properties and demiclosedness principle for this class of mappings in the framework of uniformly CONVEX Banach spaces. We further propose a new iterative method for approximating a common fixed point of two modified generalized α,-nonexpansive mappings and present some weak and strong convergence theorems for these mappings in uniformly CONVEX Banach spaces. In addition, we apply our result to solve a CONVEX-constrained minimization PROBLEM, VARIATIONAL INEQUALITY and SPLIT feasibility PROBLEM and present some numerical experiments in infinite dimensional spaces to establish the applicability and efficiency of our proposed algorithm. The obtained results in this paper improve and extend some related results in the literature.

In this paper, we obtain Jensen's INEQUALITY for GG-CONVEX functions. Also, we get inequalities alike to Hermite-Hadamard INEQUALITY for GG-CONVEX functions. Some examples are given.