Some fixed point results via auxiliary functions on orthogonal metric spaces and application to homotopy

Nurcan Bilgili Gungor; Nurcan Bilgili Gungor

doi:10.3934/math.2022815

AIMS Mathematics

2022, Volume 7, Issue 8: 14861-14874. doi: 10.3934/math.2022815

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Research article

Some fixed point results via auxiliary functions on orthogonal metric spaces and application to homotopy

Nurcan Bilgili Gungor ^,

Department of Mathematics, Faculty of Science and Arts, Amasya University, Amasya 05100, Türkiye

Received: 18 February 2022 Revised: 11 May 2022 Accepted: 24 May 2022 Published: 10 June 2022
MSC : 47H10, 54H25

In 2017, the concepts of orthogonal set and orthogonal metric spaces are presented. And an extension of Banach fixed point theorem is proved in this type metric spaces. Further in 2019, on orthogonal metric spaces, some fixed point theorems via altering distance functions are investigated. In this paper, presence and uniqueness of fixed points of the generalizations of contraction principle via auxiliary functions are investigated. And some consequences and an illustrative example are presented. On the other hand, homotopy theory constitute an important area of algebraic topology, but the application of fixed point results in orthogonal metric spaces to homotopy has not been done until now. As a different application in this field, the homotopy application of the one of the corollaries is given at the end of this paper.
- fixed point,
- altering distance functions,
- orthogonal contraction,
- orthogonal metric space,
- homotopy application
Citation: Nurcan Bilgili Gungor. Some fixed point results via auxiliary functions on orthogonal metric spaces and application to homotopy[J]. AIMS Mathematics, 2022, 7(8): 14861-14874. doi: 10.3934/math.2022815

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Abstract

In 2017, the concepts of orthogonal set and orthogonal metric spaces are presented. And an extension of Banach fixed point theorem is proved in this type metric spaces. Further in 2019, on orthogonal metric spaces, some fixed point theorems via altering distance functions are investigated. In this paper, presence and uniqueness of fixed points of the generalizations of contraction principle via auxiliary functions are investigated. And some consequences and an illustrative example are presented. On the other hand, homotopy theory constitute an important area of algebraic topology, but the application of fixed point results in orthogonal metric spaces to homotopy has not been done until now. As a different application in this field, the homotopy application of the one of the corollaries is given at the end of this paper.

References

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