Abstract
We introduce some generalizations of Prešić type contractions and establish some fixed point theorems for mappings satisfying Prešić-Hardy-Rogers type contractive conditions in metric spaces. Our results generalize and extend several known results in metric spaces. Some examples are included which illustrate the cases when new results can be applied while old ones cannot.
Highlights
The well-known Banach contraction mapping principle states that if (X, d) is a complete metric space and T : X → X is a self-mapping such that d (Tx, Ty) ≤ λd (x, y) (1)for all x, y ∈ X, where 0 ≤ λ < 1, there exists a unique x ∈ X such that Tx = x
We introduce some generalizations of Presictype contractions and establish some fixed point theorems for mappings satisfying Presic-Hardy-Rogers type contractive conditions in metric spaces
The well-known Banach contraction mapping principle states that if (X, d) is a complete metric space and T : X → X is a self-mapping such that d (Tx, Ty) ≤ λd (x, y) for all x, y ∈ X, where 0 ≤ λ < 1, there exists a unique x ∈ X such that Tx = x
Summary
We introduce some generalizations of Presictype contractions and establish some fixed point theorems for mappings satisfying Presic-Hardy-Rogers type contractive conditions in metric spaces. Reich [3], for mappings T : X → X, generalized Banach and Kannan fixed point theorems, using contractive condition: d (Tx, Ty) ≤ αd (x, y) + βd (x, Tx) + γd (y, Ty) , (3) Let (X, d) be a complete metric space, k a positive integer, and f : Xk → X a mapping satisfying the following contractive type condition: d
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