Abstract
AbstractWe study the existence and uniqueness of fixed points for self-operators defined in a b-metric space and belonging to the class of $(\alpha,\psi)$ ( α , ψ ) -type contraction mappings. The obtained results generalize and unify several existing fixed point theorems in the literature.
Highlights
1 Introduction and preliminaries Very recently, we studied in [ ] the existence and uniqueness of fixed points for selfoperators defined in a metric space and belonging to the class of (α, ψ)-type contraction mappings
We proved that the class of α-ψtype contractions includes large classes of contraction-type operators, whose fixed points can be obtained by means of the Picard iteration
The aim of this paper is to extend the obtained results in [ ] to self-operators defined in a b-metric space
Summary
Introduction and preliminariesVery recently, we studied in [ ] the existence and uniqueness of fixed points for selfoperators defined in a metric space and belonging to the class of (α, ψ)-type contraction mappings (see [ – ] for some works in this direction). Our first main result is the following fixed point theorem which requires the continuity of the mapping T.
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