2017
DOI: 10.1515/tmj-2017-0006
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New fixed point results in rectangular metric space and application to fractional calculus

Abstract: In this paper, we introduce α − ψ type contractive mapping in rectangular metric space satisfying certain admissibility conditions and prove a fixed point result for such mapping in complete and Hausdorff rectangular metric space. Some examples are given to justify our result. Also we have shown that the existence of solution of a nonlinear fractional differential equation can be guaranteed, as an application of our result.

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Cited by 8 publications
(12 citation statements)
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“…We observed that the proof of Theorem 3.2 (step 2) given in [11] is not correct. In this paper, we give its rigorous proof for a general case, that is, in the case of α−ψcontractive mappings using the concept of C-functions.…”
Section: Mathematical Preliminariesmentioning
confidence: 96%
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“…We observed that the proof of Theorem 3.2 (step 2) given in [11] is not correct. In this paper, we give its rigorous proof for a general case, that is, in the case of α−ψcontractive mappings using the concept of C-functions.…”
Section: Mathematical Preliminariesmentioning
confidence: 96%
“…Most recently, two different generalizations of α-admissible mapping were given in which the author Ansari [2] used the idea of C-class functions, whereas Budhia et al [11] used a rectangular metric. Following the ideas from [11] and [2], we provide new fixed point results in generalized metric spaces, which are also utilized to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay.…”
Section: Introductionmentioning
confidence: 99%
“…In (Budhia et al, 2017), the authors proved the following result: Theorem 1. Let (X, d r ) be a Hausdorff and complete rectangular metric space, and let T : X → X be an α−admissible mapping with respect to η.…”
Section: Introductionmentioning
confidence: 99%
“…partial metric space, b-metric, partial b-metric, extended b-metric, rectangular metric, rectangular b-metric, Gmetric, G b −metric, S-metric, S b −metric, cone metric, cone b-metric, fuzzy metric, fuzzy b-metric, probabilistic metric, etc. For more details on all variants of generalized metric spaces, see (Budhia et al, 2017), (Collaco & Silva, 1997).…”
Section: Introductionmentioning
confidence: 99%
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