COUPLED COINCIDENCE RESULTS IN A-METRIC SPACE SATISFYING GERAGHTY-TYPE CONTRACTION

Authors

  • MAIREMBAM BINA DEVI Author

DOI:

https://doi.org/10.5281/xxkq0a27

Abstract

In this paper, we employ a new concept of generalised compatibility of a pair of mappings defined on a product A-metric space. Further,
we prove some coupled coincidence point theorems in the setting of A-metric
space satisfying Geraghty-type contraction. Some results are also given in the
form of corollaries. Our results generalise corresponding results of metric space
and S-metric space into A-metric space.

References

[1] Shaban Sedghi, Nabi Shobe and Abdelkrim Aliouche, A generalization of fixed point theorems

in S-metric spaces, Matematiki Vesnik, 64, 3 (2012), 258-266.

[2] Mujahid Abbas, Bashir Ali and Yusuf I Suleiman, Generalized coupled common fixed point

results in partially ordered A-metric spaces, Fixed Point Theory and Applications (2015)

2015:64.

[3] Nizar Souayah and Nabil Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Computer Sci. 16 (2016), 131-139.

[4] Shaban Sedghi, Abdolsattar Gholidahnch, Tatjana Dosenovic and Jamileh Esfahni, Common

fixed point of four maps in Sb-metric spaces, Journal of Linear and Topological Algebra, Vol.

05, No. 02, 2016, 93-104.

[5] Yumnam Rohen, Tatjana Dosenovic and Stojan Radenovic, A note on the paper ”A fixed

point theorems in Sb-metric spaces by Nizar Souayah and Nabil mlaiki”, Filomat 31:11

(2017), 3335-3346.

[6] Kh Bulbul, Yumnam Rohen and T. Chhatrajit Singh, Coupled fixed point theorems in Gbmetric space satisfying some rational contractive conditions, Springer Plus (2016) 5: 1261.

[7] N. Mlaiki and Yumnam Rohen, Some Coupled fixed point theorems in partially ordered Abmetric space, J. Nonlinear Sci. Appl., bf 10 (2017), 1731-1743.

[8] N. Priyobarta, Yumnam Rohen amd N. Mlaiki, Complex valued Sb-metric spaces, Journal of

Mathematical Analysis, 8, 3 (2017), 13-24.

[9] H. K. Nashine, Yumnam Rohen and Th. Chhatrajit, Common coupled fixed point theorems of

two mappings satisfying generalised contractive condition in cone metric space, International

Journal of Pure and Applied Mathematices, 106(3) (2016) 791-799.

[10] Laishram Shanjit, Yummam Rohen, Th. Chhatrajit and P. P. Murthy, Coupled fixed point

theorems in partially ordered multiplicative metric space and its application, International

Journal of Pure and Applied Mathematices, 108(1) (2016) 49-62.

[11] Bulbul Khomdram and Yumnam Rohen, Quadruple common fixed point theorems in Gbmetric space, International Journal of Pure and Applied Mathematices, 109(2) (2016) 279-

293.

[12] Guo, D. and Lakshmikantham, V., Coupled Fixed Points of Nonlinear Operators with Applications, Nonlinear Analysis:TMA, 11 (1987) 623-632.

[13] Bhaskar, T.G. and Lakshmikantham, V., Fixed Point Theory in partially ordered metric

spaces and applications, Nonlinear Analysis, 65 (2006) 1379-1393.

[14] M.A. Geraghty, On contractive mappings, Proceedings of the American Mathematical Society,

40(2), 1973, 604-608.

[15] M. Zhou and X. L. Liu, On coupled common fixed point theorems for nonlinear contractions

with the mixed weakly monotone property in partially ordered S-metric space, Journal of

Function Space, 2016(2016) 9 pages 1,3,5.

[16] Mi Zhou, Xiao-lan Liu, Diana Dolicanin-Dekic and Bosko Damjanovic, Coupled coincidence

point results for Geraghty-type contraction by using monotone property in partially ordered

S-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 5950-5969.

[17] Z. Kadelburg, P. Kumam, S. Radenovic and W. Sintunavarat, Common coupled fixed point

theorems for Geraghty-type contraction mappings using monotone property, Fixed Point Theory Appl., 2015(2015), 14 pages, 1,3,3.

[18] N. Priyobarta, Yumnam Rohen and Stojan Radenovic, Fixed point theorems on parametric

A-metric space, American Journal of Applied Mathematics and Statistics, 6(1), (2018), 1-5.

[19] Yumnam Rohen, N. Priyobarta, N. Mlaiki and N. Souayah, Coupled fixed point theorems in

Ab-metric spaces satisfying rational inequality, Journal of Inequalities and Special Functions,

Vol. 9, 2(2018), 41-56.

[20] Hassen Aydi, Erdal Karapnar and Zead Mustafa, Coupled coincidence point results on generalized distance in ordered cone metric spaces, Positivity, Vol. 17, Issue 4 (2013), Page

979-993.

[21] Hassen Aydi, Erdal Karapnar and Wasfi Shatanawi, Tripled coincidence point results for

generalized contractions in ordered generalized metric spaces, Fixed Point Theory and Applications, 2012, 2012:101.

[22] Hassen Aydi, Bessem Samet and Calogero Vetro, Coupled fixed point results in cone metric

spaces for w˜-compatible mappings, Fixed Point Theory and Applications, 2011, 2011:27.

Published

2026-07-18

How to Cite

[1]
MAIREMBAM BINA DEVItran. 2026. COUPLED COINCIDENCE RESULTS IN A-METRIC SPACE SATISFYING GERAGHTY-TYPE CONTRACTION. Journal of Mathematical Analysis. 16, 01 (Jul. 2026), 01–24. DOI:https://doi.org/10.5281/xxkq0a27.