ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 13 (2018), 107 -- 117
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SOME FIXED POINT THEOREMS INVOLVING RATIONAL TYPE CONTRACTIVE OPERATORS IN COMPLETE METRIC SPACES
M. O. Olatinwo and B. T. Ishola
Abstract. Let (X, d) be a complete metric space and T from X to X a mapping of X. In 1975 Dass and Gupta introduced the following rational type contractive condition to prove a generalization of Banach's Fixed Point Theorem: For α,β∈[0,1), such that α + β
d(Tx,Ty)≤ α * d(y,Ty)*(1+d(x,Tx))⁄(1+d(x,y))+β*d(x,y),
where T is continuous.
There are several generalization and extension of Dass and Gupta's result under the hypothesis that T is continuous and α + β<1.
In this paper, we prove some fixed point theorems in a complete metric space setting by employing more general rational type contractive conditions than the above one. We show in our results that the continuity of the above operator T is unnecessary and the restrictive condition that α + β
2010 Mathematics Subject Classification: 47H06, 54H25
Keywords: complete metric spaces; rational type contractive conditions.
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M. O. Olatinwo
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria.
e-mail:~memudu.olatinwo@gmail.com, molaposi@yahoo.com, polatinwo@oauife.edu.ng
B. T. Ishola
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria.
e-mail: ~isholababs44@gmail.com