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Cyclic b-Multiplicative A,B-Hardy–Rogers-Type Local Contraction and Related Results in b-Multiplicative and b-Metric Spaces

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  • Abdullah Eqal Al-Mazrooei
  • Abdullah Shoaib
  • Jamshaid Ahmad
  • Nan-Jing Huang

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.

Suggested Citation

  • Abdullah Eqal Al-Mazrooei & Abdullah Shoaib & Jamshaid Ahmad & Nan-Jing Huang, 2020. "Cyclic b-Multiplicative A,B-Hardy–Rogers-Type Local Contraction and Related Results in b-Multiplicative and b-Metric Spaces," Journal of Mathematics, Hindawi, vol. 2020, pages 1-9, October.
    • Handle: RePEc:hin:jjmath:2460702
    DOI: 10.1155/2020/2460702
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