Fixed point of Hardy-Rogers-type contractions on metric spaces with graph

Mohammed Shehu Shagari; Faryad Ali; Trad Alotaibi; Akbar Azam; Mohammed Shehu Shagari; Faryad Ali; Trad Alotaibi; Akbar Azam

doi:10.3934/era.2023033

Electronic Research Archive

2023, Volume 31, Issue 2: 675-690. doi: 10.3934/era.2023033

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Fixed point of Hardy-Rogers-type contractions on metric spaces with graph

1.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia
3.
Department of Mathematics and Statistics, Taif University, Saudi Arabia
4.
Department of Mathematics, Grand Asian University, Sialkot, 7KM, Pasrur Road, Sialkot 51310, Pakistan

Academic Editor: Sibo Cheng

Received: 02 September 2022 Revised: 04 November 2022 Accepted: 13 November 2022 Published: 21 November 2022

This paper presents a novel concept of $ G $-Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones.
- fixed point,
- picard operator,
- directed graph,
- Hardy-Rogers contraction
Citation: Mohammed Shehu Shagari, Faryad Ali, Trad Alotaibi, Akbar Azam. Fixed point of Hardy-Rogers-type contractions on metric spaces with graph[J]. Electronic Research Archive, 2023, 31(2): 675-690. doi: 10.3934/era.2023033

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Abstract

This paper presents a novel concept of $ G $-Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones.

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