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.
Highlights
The notion of α-admissibility plays one of the main idea in the filed of mathematics to launch many contractions for self-mappings on a set X with a metric d.This amazing concept was defined by Samet et al [4]
Thereafter, many authors studied a lot of fixed point results related to contractions depending on α-admissibility
In this our paper we launch the notion of α − ψ-contractive type mappings in the context of cone b-metric spaces over Banach algebra
Summary
The notion of α-admissibility plays one of the main idea in the filed of mathematics to launch many contractions for self-mappings on a set X with a metric d (see [1,2,3] and references therein). Thereafter, many authors studied a lot of fixed point results related to contractions depending on α-admissibility (see for instance [5,6,7,8,9,10,11]). In this our paper we launch the notion of α − ψ-contractive type mappings in the context of cone b-metric spaces over Banach algebra. For other interesting results in the context of metric and b-metric spaces (see [12,13,14,15,16])
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