Abstract
Samet et al. in (Nonlinear Anal. 75:2154-2165, 2012) introduced the concepts of α-ψ-contractive type mappings and α-admissible mappings in metric spaces. The purpose of this paper is to present a new class of almost contractive mappings called almost generalized \((\alpha\mbox{-}\psi\mbox{-}\varphi\mbox {-}\theta)\)-contractive mappings and to establish some fixed and common fixed point results for this class of mappings in complete ordered b-metric spaces. Our results improve and generalize several known results from the current literature and its extension. Moreover, an application to integral equations is given here to illustrate the usability of the obtained results.
Highlights
It is well known that the Banach contraction principle has been improved in different directions at different spaces by mathematicians over the years
It should be noted that the study of common fixed points of mappings satisfying certain contractive conditions has been at the center of rigorous research activity
First, we introduce the concept of almost generalized (α-ψ-φ-θ )-contractive mappings, and we prove some common fixed point and coincidence fixed point theorems for this class of mappings in partially ordered complete b-metric spaces
Summary
It is well known that the Banach contraction principle has been improved in different directions at different spaces by mathematicians over the years.
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