Fixed Points of Multivalued Nonself Almost Contractions

Abstract

We consider multivalued nonself-weak contractions on convex metric spaces and establish the existence of a fixed point of such mappings. Presented theorem generalizes results of M. Berinde and V. Berinde (2007), Assad and Kirk (1972), and many others existing in the literature.

Fixed points of multivalued nonself almost contractions in metric-like spaces

“…In this paper, we extend the obtained results in [3] to the class of convex metric-like spaces. Mention that the concept of Hausdorff metric like was introduced in a very recent paper of Aydi et al [4].…”

“…They [5] proved the Banach's contraction principle for nonself multivalued mappings. For other results for multivalued nonself mappings, see [3,9,10,14,[17][18][19]. On the other hand, Berinde [6,7] introduced a new class of self mappings usually called weak contractions or almost contractions.…”

“…Recently, Alghamdi et al [3] introduced the notion of multivalued nonself almost contractions as follows. Alghamdi et al [3] proved the following fixed point theorem for multivalued nonself almost contractions on convex metric spaces.…”

“…Alghamdi et al [3] proved the following fixed point theorem for multivalued nonself almost contractions on convex metric spaces.…”

Common fixed point theorems for generalized contraction involving rational expressions in complex valued metric spaces

“…There are in the literature a great number of generalizations of the Banach contraction principle (see [1,2] and others). Some generalizations of the notion of a metric space have been proposed by some authors, such as, rectangular metric spaces, semi metric spaces, pseudo metric spaces, probabilistic metric spaces, fuzzy metric spaces, quasi metric spaces, quasi semi metric spaces, D-metric spaces, and cone metric spaces (see [5]- [10]).…”