Cyclic \(b\)-multiplicative \((A,B)\)-Hardy-Rogers-type local contraction and related results in \(b\)-multiplicative and \(b\)-metric spaces (Q2221855)

Summary: 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.