Cyclic b-Multiplicative A,B-Hardy–Rogers-Type Local Contraction and Related Results in b-Multiplicative and b-Metric Spaces - Abdullah Eqal Al-Mazrooei; Abdullah Shoaib; Jamshaid Ahmad (Journal of Mathematics)
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.