Abstract
Abstract In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces. The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results existing in literature. MSC:47H10, 54H25.
Highlights
The Banach contraction principle [ ] is a basic result on fixed points for contractive-type mappings
There have been a lot of fixed point results dealing with mappings satisfying diverse types of contractive inequalities
Various researchers have worked on different types of inequalities having continuity on mapping or not on different abstract spaces viz. metric spaces [ – ], convex metric spaces [ ], ordered metric spaces [ ], cone metric spaces [, ], generalized metric spaces [, ], b-metric spaces [ – ] and many more
Summary
The Banach contraction principle [ ] is a basic result on fixed points for contractive-type mappings. In , Kannan [ ] proved that if (X, d) is a complete metric space, every K - contraction on X has a unique fixed point. Various researchers generalize and/or extend Kannan and Chatterjea type contraction mappings to obtain fixed point results in abstract spaces (see [ , , , , , , – ] and references cited therein). We generalize and extend the Kannan and Chatterjea type contractions with some auxiliary functions to obtain some new fixed point results in the framework of b-metric spaces. Let (X, ρ) be a metric space, and d(x, y) = (ρ(x, y))p, where p ≥ is a real number. {d(Txn+ , Txn)} is a decreasing sequence of nonnegative real numbers and it is convergent.
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