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

Waleed M. Alfaqih; Abdullah Aldurayhim; Mohammad Imdad; Atiya Perveen; Waleed M. Alfaqih; Abdullah Aldurayhim; Mohammad Imdad; Atiya Perveen

doi:10.3934/math.2020435

AIMS Mathematics

2020, Volume 5, Issue 6: 6766-6781. doi: 10.3934/math.2020435

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Research article

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

1.
Department of Mathematics, Aligarh Muslim University, Aligarh, India
2.
Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia

Received: 19 June 2020 Accepted: 21 August 2020 Published: 01 September 2020
MSC : 47H10, 54H25

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.
- fixed point,
- multidimensional fixed point,
- implicit function,
- binary relation,
- ordinary differential equations
Citation: Waleed M. Alfaqih, Abdullah Aldurayhim, Mohammad Imdad, Atiya Perveen. Relation-theoretic fixed point theorems under a new implicit function with applications to ordinary differential equations[J]. AIMS Mathematics, 2020, 5(6): 6766-6781. doi: 10.3934/math.2020435

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Abstract

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.

References

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