Fixed Point Theorems on Spaces Endowed with Vector-Valued Metrics

Abstract

The purpose of this work is to present some local and global fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics. The results are extensions of some theorems given by Perov 1964, Bucur et al. 2009, M. Berinde and V. Berinde 2007, O'Regan et al. 2007 , and so forth.

A multivalued version of Krasnoselskii’s theorem in generalized Banach spaces

“…Therefore, the aim of this paper is to present a multivalued version of Krasnoselskii's theorem in vector Banach spaces and a nice existence result for a FredholmVolterra type integral inclusions system. Now, we recall some basic results (see [2], [8] and [28]), which are needed for the main results of this paper. Notice that in [28] and [8], are pointed out some advantages of a vector-valued norm with respect to the usual scalar norms.…”

“…Now, we recall some basic results (see [2], [8] and [28]), which are needed for the main results of this paper. Notice that in [28] and [8], are pointed out some advantages of a vector-valued norm with respect to the usual scalar norms. .…”

Ulam-Hyers stability for coupled fixed points of contractive type operators

“…The approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. For related results to Perov's fixed point theorem and for some generalizations and applications of it we refer to [3], [4], [13].…”

Ulam-Hyers stability theorem by tripled fixed point theorem

“…We are also studying Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces. For related results to Perov's fixed point theorem and for some generalizations and applications of it we refer to [7], [9], [25]. …”