In this work, we extend Minty's type lemma for a class of generalized vector quasi-equilibrium problems in Hausdorff topological vector spaces and establish some results on existence of solutions both under compact and noncompact assumption by using 1-person game theorems.

In this paper, we study a generalized monotone mapping, which is the sum of cocoercive and monotone mapping. The resolvent operator associated with generalized monotone mapping is defined, and some of its properties are discussed. We employ the equivalent formulation of generalized set-valued variational inclusion problems and resolvent equations to show the existence of a solution. In addition, we create an iterative algorithm for the convergence of resolvent equations and solving generalized set-valued variational inclusion problem. An example has also been provided to support the main result.

<abstract><p>In the present article, we study a vector optimization problem involving convexificator-based locally Lipschitz approximately convex functions and give some ideas for approximate efficient solutions. In terms of the convexificator, we approximate Stampacchia-Minty type vector variational inequalities and use them to describe an approximately efficient solution to the nonsmooth vector optimization problem. Moreover, we give a numerical example that attests to the credibility of our results.</p></abstract>

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