Abstract
Introduction/purpose: This paper establishes some new results of Piri-Kumam-Dung-type mappings in a complete metric space.The goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F-contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion:The authors believe that the obtained results represent a significant improvement of many known results in the existing literature.
Highlights
Introduction and preliminariesA fundamental role in the foundations of the constructions is played by the fixed point theorems in metric spaces
We show the existence of the fixed point
We believe that this is a significant improvement of the known results in the existing literature
Summary
Introduction and preliminariesA fundamental role in the foundations of the constructions is played by the fixed point theorems in metric spaces. It shows that in a complete metric space, each contractive mapping has a unique fixed point. Theorem 1.1 (Wardowski, 2012) Let , be a complete metric space and S : be an F contraction.
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