Results pertaining to fixed points in ordered metric spaces with auxiliary functions and application to integral equation

N. Seshagiri Rao; Ahmad Aloqaily; Nabil Mlaiki; N. Seshagiri Rao; Ahmad Aloqaily; Nabil Mlaiki

doi:10.3934/math.2024528

AIMS Mathematics

2024, Volume 9, Issue 5: 10832-10857. doi: 10.3934/math.2024528

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Research article

Results pertaining to fixed points in ordered metric spaces with auxiliary functions and application to integral equation

1.
Department of Mathematics and Statistics, School of Applied Science and Humanities, Vignan's Foundation for Science, Technology and Research, Vadlamudi, Guntur, Andhra Pradesh 522213, India; seshu.namana@gmail.com
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; nmlaiki2012@gmail.com
3.
School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney 2150, Australia; maloqaily@psu.edu.sa

Received: 03 February 2024 Revised: 10 March 2024 Accepted: 13 March 2024 Published: 19 March 2024
MSC : 47H10, 54H25

This paper delves into fixed point findings within a complete partially ordered $ b $-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper.
- weakly contractive conditions,
- $ b $-metric space,
- fixed point,
- compatible mappings,
- coincidence points,
- coupled coincidence points
Citation: N. Seshagiri Rao, Ahmad Aloqaily, Nabil Mlaiki. Results pertaining to fixed points in ordered metric spaces with auxiliary functions and application to integral equation[J]. AIMS Mathematics, 2024, 9(5): 10832-10857. doi: 10.3934/math.2024528

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Abstract

This paper delves into fixed point findings within a complete partially ordered $ b $-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper.

References

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