Relation-theoretic fixed point theorems under a new implicit function with applications to ordinary differential equations

In this paper, we introduce a new implicit function without any continuity requirement and utilize the same to prove unified relation-theoretic fixed point results. We adopt some examples to exhibit the utility of our implicit function. Furthermore, we use our results to derive some multidimensional...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 6; pp. 6766 - 6781
Main Authors M. Alfaqih, Waleed, Aldurayhim, Abdullah, Imdad, Mohammad, Perveen, Atiya
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
binary relation
fixed point
implicit function
multidimensional fixed point
ordinary differential equations
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Summary:In this paper, we introduce a new implicit function without any continuity requirement and utilize the same to prove unified relation-theoretic fixed point results. We adopt some examples to exhibit the utility of our implicit function. Furthermore, we use our results to derive some multidimensional fixed point results. Finally, as applications of our results, we study the existence and uniqueness of solution for a first-order ordinary differential equations.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020435