SOME COUPLED FIXED POINT THEOREMS SATISFYING CONTRACTIVE CONDITION OF RATIONAL TYPE VIA MIXED MONOTONE MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
Keywords:
monotone property, rational contractions, Coupled fixed point, Partially ordered metric spaceAbstract
In this article, we prove the existence and uniqueness of coupled fixed point for nonlinear contractive mappings of rational type in the context of mixed monotone mappings for metric space, which is endowed with a partial order. The outcome ofour findings is an improvement to the available results in the literature.
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References
R. Kannan; Some results on fixed points, Amer. Math. Soc., 76, (1969), 405-408.
H. Chatterji; On generalization of Banach contraction principle, Indian J. Pure. App. Math., 10, (1979), 400-403.
B. K.Dass and S. Gupta; An extension of Banach contraction principle through rational expression, Indian J. Pure. App. Math., 6, (1975), 1455-1458.
R. N.Seshagiri andK. Kalyani; Fixed point theorems in partially ordered metric spaces with rational expressions, Information Science Letters, 10, (2021), 451-460.
S. Chandok and J.K. Kim;Fixed point theorems in ordered metric spaces for generalized contraction mappings satisfying rational type expressions, Nonlinear Funct. Anal. and Appl., 17, (2012), 301-306.
R. N. Seshagiri, K. Kalyani and M. Belay M; On fixed point theorems of monotone functions in ordered metric spaces, J. of Anal., (2021), 14 pages.
R. N. Seshagiri and K. Kalyani; Coupled fixed point theorems with rational expressions in partially ordered metric spaces, J. of Anal., 28, 4, (2020), 1085-1095.
S. Chandok; Some common fixed point results for rational type contraction mappings in partially ordered metric spaces, Math. Bohem, 138(4), (2013), 407-413.
R. N.Seshagiri, K.Kalyani and K.Khatri; Contractive mappings theorems in partially ordered metric space, Cubo, 22(2), (2020), 203-214.
J. Harjani, B.Lopez 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., Article ID 190701, (2010), 8 pages.
A.C. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to marix
equations, Proceedings of the American Mathematical Society,132, 5, 1435-1443,2004.
J.J. Nieto, R. Rodriguez-Lopez,Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Oder, 22, 3, 223-239,2005.
T.G. Bhaskar and V.Lakshmikantham; Fixed points theorems in partially ordered metric spaces and applications. Nonlinear Anal., Theory Methods Appl., 65, (2006), 1379-1393.
R. N. Seshagiri and K. Kalyani; Unique fixed point theorems in partially ordered metric spaces, Heliyon, 6, 11, (2020), 7 pages.
M. Arshad, E. Karapinar and J. Ahmad; Some unique fixed point theorems for rational contractions in partially ordered metric spaces, J. of Inequalities and Appl., (2013), 248-255.
K. Kalyani, R. N.Seshagiri and M. Belay On fixed point theorems of monotone functions in ordered metric spaces, J. of Anal., (2021), 12 pages.
R. N. Seshagiri, K. Kalyani and K. Prasad; Coincidence points in ordered metric spaces and its application, Punjab University J. of Math., 54(1), (2022), 33 – 43.
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