Hybrid fixed point theorems of graphic contractions with applications

Jamilu Abubakar Jiddah; Mohammed Shehu Shagari; Maha Noorwali; Ahmad Aloqaily; Nabil Mlaiki

doi:10.1016/j.heliyon.2024.e31269

Hybrid fixed point theorems of graphic contractions with applications

Heliyon. 2024 May 16;10(10):e31269. doi: 10.1016/j.heliyon.2024.e31269. eCollection 2024 May 30.

Authors

Jamilu Abubakar Jiddah¹, Mohammed Shehu Shagari², Maha Noorwali³, Ahmad Aloqaily^{4

5}, Nabil Mlaiki⁴

Affiliations

¹ Department of Mathematics, School of Physical Sciences, Federal University of Technology, Minna, Nigeria.
² Department of Mathematics, Faculty of Physical Sciences Ahmadu Bello University, Zaria, Nigeria.
³ Department of Mathematics, King Abdulaziz University Jeddah, Saudi Arabia.
⁴ Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
⁵ School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, 2150, Australia.

Abstract

In this work, a family of hybrid contractions, termed Jaggi-type hybrid (ℵ-τ)-contractive mapping is proposed in metric space equipped with a graph and new conditions under which the mapping is a Picard operator are studied. The novel ideas proposed in this manuscript are exemplified to display the validity of the presented results and to show how they differ from the existing ones. Additionally, some corollaries which reduce our proposed notion to some recently announced concepts in the existing findings are indicated and examined. Finally, we study Ulam-type stability for the fixed point equations with hybrid contractions.

Keywords: 05C40; 46N40; 46T99; 47G10; 54G25; Fixed point; Graphic contraction; Hybrid contractive mapping; Jaggi-type contractive mapping; Picard operator; Ulam stability.