Some Applications via Common Coupled Fixed Points in \(G\)-Metric Spaces With Altering Distance Functions

Authors

DOI:

https://doi.org/10.26713/cma.v14i2.2204

Keywords:

Common coupled fixed point, Altering distance function

Abstract

In this article, we give some applications to integral equations as well as homotopy theory via common coupled fixed point theorems in complete \(G\)-metric space which involve altering distance function is established. We also furnish an example which supports our main result. Our results extend, unify and generalize some existing results in the current literature.

Downloads

Download data is not yet available.

References

M. Abbas, M. A. Khan and S. N. Radenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Applied Mathematics and Computation 217(1) (2010), 195 – 202, DOI: 10.1016/j.amc.2010.05.042.

M. Abbas, T. Nazir, W. Shatanawi and Z. Mustafa, Fixed and related fixed point theorems for three maps in G-metric spaces, Hacettepe Journal of Mathematics and Statistics 41(2) (2012), 291 – 306, URL: https://dergipark.org.tr/tr/download/article-file/86447.

M. Abbas, T. Nazir and P. Vetro, Common fixed point results for three maps in G-metric spaces, Filomat 25(4) (2011), 1 – 17, DOI: 10.2298/FIL1104001A.

R. P. Agarwal and E. Karapınar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory and Applications 2013 (2013), Article number: 2, DOI: 10.1186/1687-1812-2013-2.

H. Aydi, B. Damjanovic, B. Samet and W. Shatanawi, Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Mathematical and Computer Modelling 54(9-10) (2011), 2443 – 2450, DOI: 10.1016/j.mcm.2011.05.059.

H. Aydi, M. Postolache and W. Shatanawi, Coupled fixed point results for (ψ,φ)-weakly contractive mappings in ordered G-metric spaces, Computers & Mathematics with Applications 63(1) (2012), 298 – 309, DOI: 10.1016/j.camwa.2011.11.022.

L. Ciric and V. Lakshmikantham, Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stochastic Analysis and Applications 27(6) (2009), 1246 – 1259, DOI: 10.1080/07362990903259967.

T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods & Applications 65(7) (2006), 1379 – 1393, DOI: 10.1016/j.na.2005.10.017.

M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30 (1984), 1 – 9, DOI: 10.1017/S0004972700001659.

J. K. Kim and S. Chandok, Coupled common fixed point theorems for generalized nonlinear contraction mappings with the mixed monotone property in partially ordered metric spaces, Fixed Point Theory and Applications 2013 (2013), Article number: 307, DOI: 10.1186/1687-1812-2013-307.

V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods & Applications 70(12) (2009), 4341 – 4349, DOI: 10.1016/j.na.2008.09.020.

N. V. Luong and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Analysis: Theory, Methods & Applications 74(3) (2011), 983 – 992, DOI: 10.1016/j.na.2010.09.055.

Z. Mustafa, M. Khandagji and W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Scientiarum Mathematicarum Hungarica 48(3) (2011), 304 – 319, DOI: 10.1556/sscmath.48.2011.3.1170.

Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory and Applications 2008 (2008), Article number: 189870, DOI: 10.1155/2008/189870.

Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point results in G-metric spaces, International Journal of Mathematics and Mathematical Sciences 2009 (2009), Article ID: 283028, DOI: 10.1155/2009/283028.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis 7(2) (2006), 289 – 297, URL: http://yokohamapublishers.jp/online2/opjnca/vol7/p289.html.

Z. Mustafa and B. Sims, Fixed Point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory and Applications 2009 (2009), Article number: 917175, DOI: 10.1155/2009/917175.

Downloads

Published

18-09-2023
CITATION

How to Cite

Reddy, G. U., Naresh, . P., & Rao, B. S. (2023). Some Applications via Common Coupled Fixed Points in \(G\)-Metric Spaces With Altering Distance Functions. Communications in Mathematics and Applications, 14(2), 511–526. https://doi.org/10.26713/cma.v14i2.2204

Issue

Section

Research Article