We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

We introduce a class of generalized vector quasivariational-like inequality problems in Banach spaces. We derive some new existence results by using KKM-Fan theorem and an equivalent fixed point theorem. As an application of our results, we have obtained as special cases the existence results for vector quasi-equilibrium problems, generalized vector quasivariational inequality and vector quasi-...

Abstract We describe a special class of quasi-equilibrium problems in metric spaces and propose novel simple threshold descent method for solving these problems. Due to the framework, convergence cannot be established with usual convexity or generalized assumptions. Under mild conditions, iterative procedure gives solutions problem. apply this scalar vector some classes relative optimization

We define the quasi-minimal elements of a set with respect to a convex cone and characterize them via linear scalarization. Then we attach to a general vector optimization problem a dual vector optimization problem with respect to quasi-efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem we derive vector dual problems ...

We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems are established

The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.

In this paper, we establish the regularized gap function for a class of mixed parametric vector quasi- equilibrium problems (briefly, (MPVQEP)y). Then an error bound is also provided (MPVQEP)g via under suitable assumptions. Some examples are given to illustrate our results. Our main results extend and differ from those corresponding ones in current literatures.