Some fixed point results for dualistic rational contractions

Muhammad Nazam

Pakistan

International Islamic University

Department of Mathematics and Statistics

Muhammad Arshad

Pakistan

International Islamic University

Professor of Mathematics

Department of Mathematics and Statistics

Mujahid Abbas

South Africa

University of Pretoria

Professor of Mathematics

Department of Mathematics and Applied Mathematics

Submitted: 2016-06-11

|

Accepted: 2016-08-28

|

Published: 2016-10-03

DOI: https://doi.org/10.4995/agt.2016.5920
Funding Data

Downloads

Keywords:

fixed point, dualistic partial metric, dualistic contraction of rational type

Supporting agencies:

This research was not funded

Abstract:

In this paper, we introduce a new contraction called dualistic contraction of rational type and obtain some fixed point results. These results generalize various comparable results appeared in the literature. We provide an example to show the superiority of our results over corresponding fixed point results proved in metric spaces.
Show more Show less

References:

J. Harjani, B. López and K. Sadarangani, A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Abstr. Appl. Anal. (2010), Art. ID 190701. https://doi.org/10.1155/2010/190701

H.Isik and D.Tukroglu, Some fixed point theorems in ordered partial metric spaces, Journal of Inequalities and Special Functions 4 (2013), 13-18. https://doi.org/10.1186/1687-1812-2013-51

S. G. Matthews, Partial Metric Topology, in proceedings of the $11^{t}h$ Summer Conference on General Topology and Applications, 728 (1995), 183-197, The New York Academy of Sciences. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x

M. Nazam and M.Arshad, On a fixed point theorem with application to integral equations, International Journal of Analysis 2016 (2016) Article ID 9843207, 7 pages. https://doi.org/10.1155/2016/9843207

J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22, no. 3 (2005), 223-239. https://doi.org/10.1007/s11083-005-9018-5

S. Oltra and O.Valero, Banach's fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste 36 (2004),17-26.

S. J. O'Neill, Partial metric, valuations and domain theory, Annals of the New York Academy of Science, 806 (1996), 304-315. https://doi.org/10.1111/j.1749-6632.1996.tb49177.x

A. C. M. Ran and M. C. B. Reuring, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132, no. 5 (2004), 1435-1443. https://doi.org/10.1090/S0002-9939-03-07220-4

O. Valero, On Banach fixed point theorems for partial metric spaces, Applied General Topology 6, no. 2 (2005), 229-240. https://doi.org/10.4995/agt.2005.1957

Show more Show less