On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

Abstract

We introduce the notion of α -admissibility of mappings on cone b-metric spaces using Banach algebra with coefficient s, and establish a result of the Hardy-Rogers theorem in these spaces. Furthermore, using symmetry, we derive many recent results as corollaries. As an application we prove certain fixed point results in partially ordered cone b-metric space using Banach algebra. Also, we use our results to derive and prove some real world problems to show the usability of our obtained results. Moreover, it is worth noticing that fixed point theorems for monotone operators in partially ordered metric spaces are widely investigated and have found various applications in differential, integral and matrix equations.

The Pb-cone metric spaces over Banach algebra with applications

“…They provided an example to explain the non-equivalence of the fixed point result between cone metric spaces over Banach algebra and cone b-metric space over Banach algebra. Reader may also refer [34].…”

Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2

“…Remark 33. Our Theorem 32 generalizes Theorem 1 in [38] from a cone b -metric space over a Banach algebra to a cone b 2 -metric space over a Banach algebra.…”

New coupled and common coupled fixed point results with generalized c -distance on cone b -metric spaces

“…They provided and build up some topological properties which will be needed to upgrade and prove some results in literature to cone b-metric space. This work, opened a new area in analysis which stimulated many authors to generalized several well-known comparable results in literature under many type of contractive conditions to cone b-metric spaces (see [7,13,20,23,25,33,[35][36][37] and the references therein).…”