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In this paper, we developed a new type iterative scheme to approximate 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 proved that the sequence generated by the proposed iterative method converges strongly to a common solution of split monotone variational inclusion, variational inequality and fixed point problems. Furthermore, we give some consequences of the main result. Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm. The result presented in this paper unifies and extends some known results in this area. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized exponential fuzzy vector variational-like inequalities in Euclidean spaces. We construct an example to illustrate the main problem. We define a new class of αg-relaxed exponentially (γ η)-monotone mapping in fuzzy environment. We prove the existence of solutions to generalized exponential vector variational-like inequality with fuzzy mappings by using KKM-technique. Further, we give some consequences of the main result. The results presented in this paper unifies and extends some known results in this area. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a viscosity implicit midpoint rule to approximate the solution of an attractive fixed point problem for a nonexpansive mapping in a real Hilbert space. Further, we obtain a weak convergence theorem for the sequence generated by the proposed iterative scheme. Furthermore, we derive some consequence from our main result. The result presented in this paper extended and unify many of the previously known results in this area. [ABSTRACT FROM AUTHOR]

In this paper, we introduced and study an operator mixed vector equilibrium problem which is a combination of an operator vector variational inequality and an operator vector equilibrium problem. We prove an existence result for our problem using KKM-theorem and vector 0-diagonally quasi convexity and another existence result without using KKM-theorem. An example is constructed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a generalized variational-like inequality problem in topological vector spaces. We prove an existence result for generalized variational-like inequality problem using KKM-theorem and we show its equivalence with another variational-like inequality problem using relaxed η-α-monotone mapping. Our result improve and extend some corresponding results of [1, 9, 10, 17, 22, 23]. [ABSTRACT FROM AUTHOR]

In this paper, we study the weak and strong versions of generalized composite vector equilibrium problem in Hausdorff topological vector spaces. The generalized KKM-theorem due to [3] is applied to solve both the problems in non-compact setting. Some special cases are listed and examples are constructed. [ABSTRACT FROM AUTHOR]

In this paper, we consider random generalization of completely generalized nonlinear variational-like inclusions and propose an iterative algorithm for computing their approximate solutions. We prove that the approximate solutions obtained by proposed algorithm converge to the exact solution of our problem. [ABSTRACT FROM AUTHOR]