### COMMON FIXED POINTS OF A PAIR OF SELFMAPS SATISFYING CERTAIN WEAKLY CONTRACTIVE INEQUALITY INVOLVING RATIONAL TYPE EXPRESSIONS VIA TWO AUXILIARY FUNCTIONS IN PARTIALLY ORDERED METRIC SPACES

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#### Abstract

In this paper, we prove the existence of coincidence and common fixed points of a pair of selfmaps satisfying certain weakly contractive inequality with two auxiliary functions involving rational type expressions in partially ordered metric spaces. These results extend some of the known existing results in the literature from a single selfmap to a pair of selfmaps. Examples are provided in support of our results.

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A. Amini-Harindi, H. Emami. A xed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary dierential equations. Nonlinear Analysis, 2010, 72(5): 2238-2242.

G. V. R. Babu, P. D. Sailaja. A xed point theorem of generalized weakly contractive maps in orbitally complete metric spaces. Thai Journal of Mathematics, 2011, 9(1): 1-10.

G. V. R. Babu, K.K. M. Sarma, P. H. Krishna. Fixed points of - weak Geraghty contractions in partially ordered metric spaces. Journal of Advanced Research in Pure Mathematics, 2014, 6(4): 9-23. doi: 10.5373/jarpm.1896.120413.

I. Cabrera, J. Harjani, K. Sadarangani, A xed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara. 2013, 59 : 251-258. doi: 10.1007/s11565-013-0176.

S. Chandok, B. S. Choudhury, N. Metiya. Fixed point results in ordered metric spaces for rational type expressions with auxillary functions. Journal of the Egyptian Mathematical Society. 2014, 23(1): 95-101.

B. K. Dass, S. Gupta, An extension of Banach contraction principle through rational expressions, Indian J. Pure and Appl. Math., 1975, 6: 1455-1458.

J. Harjani, B. Lopez, K. Sadarangani. Fixed point theorems for weakly contractive mappings in ordered metric spaces. Comp. and Math., with Appl., 2011, 61:790-796.

J. Harjani, K. Sadarangani. Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Analysis, 2009, 71: 3403-3410. doi: 10.1016/j.na.2009.01.240.

J. Harjani, K. Sadarangani. Generalized contractions in partially ordered metric spaces and applications to ordinary dierential equations. Nonlinear Analysis, 2010, 72: 1188-1197.

J. Jachymski, Order - Theoretic aspects of xed point theory, Hand book of metric xed point theory, Kluwer accadamic publishers, Dordrechet, (2001).

G. Jungck, Compatible mappings and common xed points", Int. J. Math. Math. Sci., 9(4), (1986), 771-779,

G. Jungck, B.E.Rhoades, Fixed points for set-valued functions with out continuity.Indian J.Pure and Appl.Math.,1998,29(3):227-238.

J. J. Nieto, R. Rodriguez-Lopez. Contractive mapping theorems in partially ordered sets and Applications to ordinary dierential equations. Order, 2005, 22(3): 223-239. doi: 10.1007/s11083-005-9018-5.

R.P. Pant, A common xed point theorem under a new condition", Indian J. Pure Appl. Math., 30(2), (1999), 147-152.

A. C. M. Ran, M. C. B. Reurings. A xed point theorem in partially ordered sets and some application to matrix equations. Proc. Amer. Math. Soc., 2004, 132: 1435-1443. doi: 10.1090/S002-9939-03-07220-4.

K. P. R. Sastry, G. V. R. Babu, K. K. M. Sarma, P. H. Krishna. Fixed points of Geraghty contractions in partially ordered metric spaces under the in uence of altering distances. IJMA, 2014 5(10): 185-195.

K. P. R. Sastry, G. V. R. Babu, K. K. M. Sarma and P. H. Krishna, Fixed points of selfmaps on partially ordered metric spaces with control functions involving rational type expressions, Journal of Advanced Research in Pure Mathematics, 2015 Vol. 7, Issue. 4: 92-102.

DOI: https://doi.org/10.22190/FUMI1703329B

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