Fixed point theorems in $C^{*}$-algebra-valued $b_{v}(‎ ‎s)$-metric spaces with application and numerical methods

Authors

  • Mohammad Hassan Saboori Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
  • Mahmoud Hassani Mashhad Branch, Islamic Azad University, Mashhad, Iran.
  • Reza Allahyari Mashhad Branch, Islamic Azad University, Mashhad, Iran.
  • Mohammad Mehrabinezhad Mashhad Branch, Islamic Azad University, Mashhad, Iran.

DOI:

https://doi.org/10.30495/jme.v0i0.1436

Keywords:

$C^{*}$-algebra, $b_{v}(s)$-metric space, Fixed point theorem, Integral equation, Contractive mapping

Abstract

‎We first introduce a novel notion named $C^{*}$-algebra-valued $b_{v}(s)$-metric spaces‎. ‎Then‎, ‎we give proofs of the Banach contraction principle‎, ‎the expansion mapping theorem‎, ‎and Jungck's theorem in $C^{*}$-algebra-valued $b_{v}(s)$-metric spaces‎. ‎As an application of our results‎, ‎we establish a result for an integral equation in a $C^{*}$-algebra-valued $b_{v}(s)$-metric space‎. ‎Finally‎, ‎a numerical method is presented to solve the proposed integral equation‎, ‎and the convergence of this method is also studied‎. ‎Moreover‎, ‎a numerical example is given to show applicability and accuracy of the numerical method and guarantee the theoretical results‎.

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Published

2020-08-06

Issue

Vol. 15

Section

Vol. 15, No. 3, (2021)

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