Fixed points of multivalued $$\alpha $$ α -admissible mappings and stability of fixed point sets in metric spaces

Abstract

In this paper we establish some fixed point results of multivalued α-admissible mappings in the framework of metric spaces. The mappings are assumed to satisfy certain rational type α−ψ-contractions. We support our main results with an example. We use Hausdorff distance in our theorems. We also study the stability of fixed point sets of above mentioned set valued contractions. By applications of the multivalued results we obtain certain fixed point theorems of singlevalued mappings.

Common fixed point results of generalized almost rational contraction mappings with an application

“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”

“…Following this trend, Samet et al [34] first introduced α-admissible mappings and then α-ψ-contractive type mappings to obtain some interesting generalizations of Banach contraction principle. For more results in this direction, we refer to [6,13,14,16,17,20,21,22,24,28,30,32] and references mentioned therein. Recently, Alizadeh et al [5] defined the concept of cyclic (α, β)-admissible mapping as follows: Definition 1.1 ( [5]).…”

Fixed Point Results for Multivalued Prešić Type Weakly Contractive Mappings

“…Dutta and Choudhury [5] established (ψ, φ)-contraction mappings and proved fixed point results of these mappings. Choudhury et al [6] proved fixed points of multivalued α-admissible mappings and stability of fixed point sets in metric spaces. Latif and Beg obtined [7] the geometric fixed points for single and multivalued mappings.…”

Fixed Point Sets of Multivalued Contractions and Stability Analysis

“…The essence of such efforts is to restrict the contractive condition to appropriate subsets of X × X, rather than assuming to be valid between arbitrary pairs of points from the metric space. This is the development which is parallel to the emergence of fixed point theory in partially ordered metric spaces where the introduction and use of the partial order in metric space also serves the same purpose [4], [11]- [16].…”