Mathematics (May 2020)

Fixed Point Results for a Selected Class of Multi-Valued Mappings under (<i>θ</i>,<i>ℛ</i>)-Contractions with an Application

  • Md Hasanuzzaman,
  • Salvatore Sessa,
  • Mohammad Imdad,
  • Waleed M. Alfaqih

DOI
https://doi.org/10.3390/math8050695
Journal volume & issue
Vol. 8, no. 5
p. 695

Abstract

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In this article, we introduce a relatively new concept of multi-valued ( θ , R ) -contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

Keywords