A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces

A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimiz...

Generalized Convex Set-Valued Maps

The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t ...

Fixed Point Theorems for Set-Valued Generalized Contractive Maps in Cone Metric Spaces

Banach’s contraction principle plays an important role in several branches of mathematics. Because of its importance for mathematical theory, it has been extended in many direction. Especially, Nadler [23] gave a generalization of Banach’s contraction principle to the case of set-valued maps in metric spaces. The author [13] obtained a generalization of Nadler’s fixed point theorem. They proved...

Generalized coincidence theory for set-valued maps

This paper presents a coincidence theory for general classes of maps based on the notion of a Φ-essential map (we will also discuss Φ-epi maps). c ©2017 All rights reserved.

Common Fixed Points of Generalized Contractive Maps in Cone Metric Spaces