Abstract
The existence of fixed points, coupled fixed points, and coupled coincidence points without the assumption of compatibility is established. The results presented in this paper extend, improve, and generalize some well-known results in the literature. Also, an example is given to show that our results are real generalizations of known ones in coupled coincidence fixed point theory. MSC:54H25, 47H10.
Highlights
1 Introduction Fixed point theorems in metric spaces play a major role for solving problems in applied mathematics and science
The Banach contraction principle is an important tool in the theory of metric spaces, it guarantees the existence and uniqueness of fixed points of certain self maps of metric spaces
In [ ] Bhaskar and Lakshmikantham introduced the concept of coupled fixed point of a function F : X × X → X which has the mixed monotone property, where X is a partially ordered metric space
Summary
Fixed point theorems in metric spaces play a major role for solving problems in applied mathematics and science.
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