Abstract
In this paper, we prove some unique fixed point results for an operator T satisfying certain rational contraction condition in a partially ordered metric space. Our results generalize the main result of Jaggi (Indian J. Pure Appl. Math. 8(2):223-230, 1977). We give several examples to show that our results are proper generalization of the existing one. MSC:47H10, 54H25, 46J10, 46J15.
Highlights
Fixed point theory is one of the famous and traditional theories in mathematics and has a broad set of applications
There have been a number of generalizations of metric spaces such as rectangular metric spaces, pseudo metric spaces, fuzzy metric spaces, quasi metric spaces, quasi semi-metric spaces, probabilistic metric spaces, D-metric spaces and cone metric spaces
Xn ∀n ∈ N, x∗ ∀n ∈ N, In this manuscript, we prove that an operator T satisfying certain rational contraction condition has a fixed point in a partially ordered metric space
Summary
Fixed point theory is one of the famous and traditional theories in mathematics and has a broad set of applications. We establish the existence of a unique fixed point of a map T by assuming only the continuity of some iteration of T.
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