Abstract
In this paper, we give an affirmative answer to an open question posed recently by Mlaiki et al. As a consequence of our results, we get some known results in the literature. We also give an application of our results to the existence of a solution of nonlinear fractional differential equations.
Highlights
Fréchet [1] introduced the axiomatic form of distance as L-space
The aim of this work is to provide an answer to the above question by providing other hypotheses required to prove the existence of a unique fixed point of the mapping T given in Question 1
We gave an affirmative answer to an open question posed recently by Mlaiki et al [Adv
Summary
Fréchet [1] introduced the axiomatic form of distance as L-space. Hausdorff [2] re-defined it as a metric space. In 1922, Banach [3] proved the existence and uniqueness of a fixed point for self-contractive mappings in a complete metric space. Inspired by the wide applications of Banach’s result, numerous extensions and generalizations of it appeared in the literature One direction of such generalizations was by generalizing the concept of a metric space itself. The concept of a controlled rectangular b-metric space was introduced in Mlaiki et al [14]. Let ( X, Dξ ) be a Dξ -complete controlled rectangular b-metric space, T : X → X be a self map on X. The aim of this work is to provide an answer to the above question by providing other hypotheses required to prove the existence of a unique fixed point of the mapping T given in Question 1. We show that condition (2) is redundant and that condition (3) can be relaxed
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