Results on Coincidence and common fixed point theorems for $ L_\mathcal{R} $ -contraction

Shahbaz Ali; Maneesha; Asik Hossain; Qamrul Haque Khan; Suhel Ahmad Khan; Shahbaz Ali; Maneesha; Asik Hossain; Qamrul Haque Khan; Suhel Ahmad Khan

doi:10.3934/math.2026104

AIMS Mathematics

2026, Volume 11, Issue 1: 2578-2594. doi: 10.3934/math.2026104

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Results on Coincidence and common fixed point theorems for $ L_\mathcal{R} $ -contraction

1.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2.
BITS-Pilani, Dubai Campus, Dubai, P.O. Box 345055, United Arab Emirates
3.
School of Applied Sciences and Humanities, Haldia Institute of Technology, Haldia 721657, India

Received: 13 November 2025 Revised: 20 December 2025 Accepted: 04 January 2026 Published: 27 January 2026
MSC : 47H10, 54H25

In this paper, we establish coincidence and common fixed point theorems for a pair of mappings $(T, S)$ that utilize the binary relation in a metric space employing the concept of a locally finitely $T$ -transitive relation together with an $ L_\mathcal{R} $ contraction. We also provide appropriate added suitable examples to establish the genuineness of our newly established results over the corresponding earlier known results.
- common fixed point and coincidence point,
- binary relation,
- $ L_\mathcal{R} $ -contraction
Citation: Shahbaz Ali, Maneesha, Asik Hossain, Qamrul Haque Khan, Suhel Ahmad Khan. Results on Coincidence and common fixed point theorems for $ L_\mathcal{R} $ -contraction[J]. AIMS Mathematics, 2026, 11(1): 2578-2594. doi: 10.3934/math.2026104

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Abstract

In this paper, we establish coincidence and common fixed point theorems for a pair of mappings $(T, S)$ that utilize the binary relation in a metric space employing the concept of a locally finitely $T$ -transitive relation together with an $ L_\mathcal{R} $ contraction. We also provide appropriate added suitable examples to establish the genuineness of our newly established results over the corresponding earlier known results.

References

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