Set-valued optimization which is an extension of vector to set-valued problems a growing branch applied mathematics. The application technics and the investigation optimality conditions has been enormous interest in research problems. In this paper we have considered Mayer type problem governed by discrete inclusion system with Lipschitzian mappings. A necessary condition for K-optimal solution...

Inverse limits with set-valued functions having graphs that are the union of mappings have attracted some attention over the past few years. In this paper we show that if the graph of a surjective set-valued function f : [0, 1] → 2[0,1] is the union of two mappings having only one point (x, x) in common such that x is not the image of any other point of the interval under f , then its inverse l...

Deguire and Lassonde [P. Deguire, M. Lassonde, Familles sélectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261–269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obt...