Fixed Point Results for a Selected Class of Multi-Valued Mappings under ( ?, ? )-Contractions with an Application

Md Hasanuzzaman, Salvatore Sessa, Mohammad Imdad and Waleed M. Alfaqih
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Md Hasanuzzaman: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Salvatore Sessa: Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
Mohammad Imdad: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Waleed M. Alfaqih: Department of Mathematics, Hajjah University, Hajjah 1729, Yemen

Mathematics, 2020, vol. 8, issue 5, 1-17

Abstract: 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: fixed point; monotone type mappings; multi-valued ? -contractions; binary relations; integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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