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The aim of this paper is two fold, first we introduce a generalized Yosida approximation operator whose structure depends on the resolvent operator introduced in [2]. Secondly, we show some of its characteristics i.e., it is Lipschitz continuous as well as strongly monotone and we discuss the graph convergence of it. Finally, we obtain the solution of a system of Yosida inclusions using these concepts. An example is constructed. [ABSTRACT FROM AUTHOR]

In this article, we consider and study a vector variational inequality involving set-valued mappings. The concepts of vector 0-diagonally convex- ity and escaping sequence are used to obtain some results for vector variational inequality involving set-valued mappings. We mention some special cases of our problem. [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]