Abstract
The aim of this paper is to define cyclic b -multiplicative Hardy–Rogers-type local contraction in the context of generalized spaces named as b -multiplicative spaces to extend various results of the literature including the main results of Yamaod et al. In this way, we apply a new generalized contractive condition only on a closed set instead of a whole set and by using b -multiplicative space instead of multiplicative metric space. We apply our results to obtain new results in b -metric spaces. Examples are given to show the usability of our results, when others cannot.
Highlights
Introduction and PreliminariesBakhtin [1] was the first who gave the idea of b-metric
Mongkolkeha and Sintunavarat [6] described the concept of multiplicative proximal contraction mapping and proved some results for such mappings
In 2017, Ali et al [13] introduced the notion of the b-multiplicative space and proved some fixed point results
Summary
Introduction and PreliminariesBakhtin [1] was the first who gave the idea of b-metric. If we take θ λ 0 in Definition 5, we say it is b-multiplicative cyclic (A, B)-Chatterjea-type local contraction on Bmb(þ°, r). If we take s 1 in Definition 5, we say it is cyclic multiplicative (A, B)-Hardy–Rogers-type local contraction on Bmb(þ°, r).
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