Fuzzy fixed point theorems for multivalued fuzzy contractions in b -metric spaces

Abstract

In this paper, we introduce the new concept of multivalued fuzzy contraction mappings in b-metric spaces and establish the existence of α-fuzzy fixed point theorems in b-metric spaces which can be utilized to derive Nadler's fixed point theorem in the framework of b-metric spaces. Moreover, we provide examples to support our main result.

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

“…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.…”

Fixed point results for fuzzy mappings in a b-metric space

“…Recently, Beg et al [7] proved the result concerning the existence of fixed points of a mapping satisfying locally contractive conditions on a closed ball (see also [8][9][10][11][12][13][14][15][16]). It is also possible that the mapping satisfies locally contractive conditions on a sequence contained in a closed ball in M. One can obtain fixed point results for such a mapping by using the suitable conditions.…”

On stability of fixed point inclusion for multivalued type contraction mappings in dislocatedb‐metric spaces with application

“…The concept of b ‐metric space was introduced by Czerwik as a generalization of metric spaces and proved the contraction mapping principle in b ‐metric spaces that is extension the famous Banach contraction principle in metric spaces. A number of authors investigated fixed point theorems in b ‐metric spaces for multivalued operator (see other works and references therein). Recently, Cossetino et al extend ℑ‐contraction in the setting of b ‐metric spaces and proved some fixed point theorems.…”

“…Afterward, Asl et al 14 extended the concept of -admissible for single valued mappings to multivalued mappings and Mohammadi et al 15 introduced the concept of -admissible for multivalued mappings, which is different from the notion of * -admissible, which has been provided in Asl et al 14 The concept of b-metric space was introduced by Czerwik 16 as a generalization of metric spaces and proved the contraction mapping principle in b-metric spaces that is extension the famous Banach contraction principle in metric spaces. A number of authors investigated fixed point theorems in b-metric spaces for multivalued operator (see other works [17][18][19][20][21][22][23] and references therein). Recently, Cossetino et al 24 extend ℑ-contraction in the setting of b-metric spaces and proved some fixed point theorems.…”