Existence of common fixed points of improved F-contraction on partial metric spaces

Muhammad Nazam; Muhammad Arshad; Mujahid Abbas

doi:10.4995/agt.2017.6776

Authors

Muhammad Nazam International Islamic University
Muhammad Arshad International Islamic University
Mujahid Abbas University of Pretoria

DOI:

https://doi.org/10.4995/agt.2017.6776

Keywords:

fixed point, improved F-contraction, integral equations, complete partial metric space

Abstract

Following the approach of F-contraction introduced by Wardowski [13], in this paper, we introduce improved F-contraction of rational type in the framework of partial metric spaces and used it to obtain a common fixed point theorem for a pair of self mappings. We show, through example, that improved F-contraction is more general than F-contraction and guarantees fixed points in those cases where F-contraction fails to provide. Moreover, we apply this fixed point result to show the existence of common solution of the system of integral equations.

Downloads

Download data is not yet available.

Author Biographies

Muhammad Nazam, International Islamic University

Department of Mathematics and Statistics

Muhammad Arshad, International Islamic University

Department of Mathematics and Statistics

Mujahid Abbas, University of Pretoria

Department of Mathematics and Applied Mathematics

References

M. Abbas, T. Nazir and S. Romaguera, Fixed point results for generalized cyclic contraction mappings in partial metric spaces, RACSAM 106 (2012), 287-297. https://doi.org/10.1007/s13398-011-0051-5

T. Abdeljawad, E. Karapinar and K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011), 1900-1904. https://doi.org/10.1016/j.aml.2011.05.014

I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778-2785. https://doi.org/10.1016/j.topol.2010.08.017

I. Altun and S. Romaguera. Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point, Applicable Analysis and Discrete Mathematics 6, no. 2 (2012), 247-256. https://doi.org/10.2298/AADM120322009A

M. Arshad, A. Hussain and M. Nazam, Some fixed point results for multivalued F-contraction on closed ball, Func. Anal.-TMA 2 (2016), 69-80

S. Chandok, Some fixed point theorems for $(alpha,beta)$-admissible Geraghty type contractive mappings and related results, Math. Sci. 9 (2015), 127-135. https://doi.org/10.1007/s40096-015-0159-4

S. H. Cho, S. Bae and E. Karapinar Fixed point theorems for $alpha$-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl. 2013, 2013:329.

M. Cosentino and P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat 28, no. 4 (2014), 715-722. https://doi.org/10.2298/FIL1404715C

A. Hussain, M. Nazam and M. Arshad, Connection of Ciric type F-contraction involving fixed point on closed ball, GU J. Sci. 30, no. 1 (2017), 283-291.

A. Hussain, H. F. Ahmad, M. Nazam and M. Arshad, New type of multivalued F-contraction involving fixed points on closed ball, J. Math. Computer Sci. 10 (2017), 246-254. https://doi.org/10.22436/jmcs.017.02.06

S. G. Matthews, Partial metric topology, in: Proceedings of the $11^{th}$ Summer Conference on General Topology and Applications, Vol. 728, pp.183-197, The New York Academy of Sciences, August, 1995.

M. Nazam, M. Arshad and C. Park Fixed point theorems for improved $alpha$-Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4436-4449.

D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. (2012) Article ID 94.