Coincidence points for a pair of ordered F-contraction mappings in ordered partial metric spaces

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DOI:

https://doi.org/10.26637/MJM0703/0010

Abstract

The concept of ordered F -contraction in an ordered metric space was introduced by Durmaz et al. [ 9 ] and became a very important result in the existing metric fixed point theory. In this paper, we prove a fixed point theorem for a pair of compatible F -contraction maps in an ordered complete partial metric spaces. In particular, the main results generalize a fixed point theorem due to Durmaz et. al. [ 9 ] to partial metric spaces. An illustrative example is provided to support the theorem.

Keywords:

Ordered partial metric spaces, F-contraction mappings, coincidence points

Mathematics Subject Classification:

Mathematics
  • Pages: 423-428
  • Date Published: 01-07-2019
  • Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

M. Abbas, B. Ali, and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory and Applications, 1 (2013): 243.

T. Abedelljawad, E. Karapinar and K. Tas, Existance and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011): 1894-1899.

O. Acar, G. Durmaz, and G. Minak. Generalized multivalued $F$-contractions on complete metric spaces, Bulletin of the Iranian Mathematical Society, 40(6)(2014): 14691478.

J. Ahmad, A. Al-Rawashdeh and A. Azam, New fixed point theorems for generalized $F$-contractions in complete metric spaces, Fixed Point Theory and Applications, 1 (2015): 80.

I. Altun, G. Minak, and H. Dag, Multivalued Fcontractions on complete metric space, J. Nonlinear Convex Anal., 16(4)(2015): 659-666.

F. Aryani, H. Mahmud, C. C. Marzuki, M Soleh, R Yendra and A. Fudholi, Continuity Function on Partial Metric Space, Journal of Mathematics and Statistics, 12(4) (2016), 271-276. DOI: 10.3844/jmssp.2016.271.276.

M. Bukatin, R. Kopperman and S. Matthews, Partial metric spaces, American Mathematical Monthly, 116 (2009): 708-718.

L. Ćirić, N. Cakic, M. Rajovic and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory and Applications, (2009)(1) 2008: Art. ID 131294, $11 mathrm{pp}$.

G. Durmaz, G. Minak and I. Altun, Fixed points of ordered $F$-contractions, Hacettepe Journal of Mathematics and Statistics, 45(1)(2016): 15-21.

J. Kessy, S. Kumar and G. Kakiko, Fixed points for hybrid pair of compatible mappings in partial metric spaces, Advances in Fixed Point Theory, 7(4) (2017): 489-499.

S. Matthews, Partial metric topology in Papers on General Topology and Applications, Eighth Summer Conference at Queens College. Eds. S. Andima et. al., Annals of the New York Academy of Sciences, 728 (1992): 183197.

J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, A journal on the Theory of ordered sets and its application, 22(3)(2005): 223-239.

D. Paesano and C. Vetro, Multi-valued F-contractions in O-complete partial metric spaces with application to Volterra type integral equation, Revista de la Real Academia de Ciencias Exactas Fisicas Naturales, 108(2)(2014): 1005-1020.

A. Ran and M. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004): 1435-1443.

D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications, 94(2012).

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Published

01-07-2019

How to Cite

Santosh Kumar. “Coincidence Points for a Pair of Ordered F-Contraction Mappings in Ordered Partial Metric Spaces”. Malaya Journal of Matematik, vol. 7, no. 03, July 2019, pp. 423-8, doi:10.26637/MJM0703/0010.