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Some ϕ-fixed point results in b-metric spaces with applications

Year 2019, , 447 - 456, 30.06.2019
https://doi.org/10.17776/csj.421975

Abstract

The fixed point theory is the most important topic in mathematics anaysis. This topic has many applications in the different fields. It demonstrates the uniqueness of the existence of a mapping and how it can be found. The Banach contraction mapping principle is most important theorem in the fixed point theory. Most authors have introduced new contractions and they proved some fixed point theorems in metric spaces. On the other hand, some authors introduced new metric spaces as a generalization of metric spaces. Later, they proved fixed point theorems which generalize the Banach contraction principle for various mappings in several metric spaces. The purpose of this study is to introduce the existence and uniqueness of ϕ-fixed point for some new contractions in complete b-metric spaces. Firstly, we presented new definitions called (F,ϕ,α,θ)_{s} and (F,ϕ,α,θ)_{s}-weak contractions in complete b-metric spaces as a generalization of metric spaces. Later, we proved ϕ-fixed point theorems for (F,ϕ,α,θ)_{s} and (F,ϕ,α,θ)_{s}-weak contractions in complete b-metric spaces. The presented theorems extend and generalize some ϕ-fixed point results which are known in the literature. As applications, we derived some fixed point results in complete partial b-metric spaces as a generalization of partial metric spaces. The results in this paper generalizes may existing results in the literature.

References

  • Hüseyin IŞIK e- mail adress: h.isik@alparslan.edu.tr, Arslan Hojat Ansari e- mail adress: analsisamirmath2@gmail.com, Wutiphol Sintunavarat e- mail adress: poom_teun@hotmail.com
Year 2019, , 447 - 456, 30.06.2019
https://doi.org/10.17776/csj.421975

Abstract

References

  • Hüseyin IŞIK e- mail adress: h.isik@alparslan.edu.tr, Arslan Hojat Ansari e- mail adress: analsisamirmath2@gmail.com, Wutiphol Sintunavarat e- mail adress: poom_teun@hotmail.com
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Details

Primary Language English
Journal Section Natural Sciences
Authors

Müzeyyen Sangurlu Sezen

Publication Date June 30, 2019
Submission Date May 8, 2018
Acceptance Date February 21, 2019
Published in Issue Year 2019

Cite

APA Sangurlu Sezen, M. (2019). Some ϕ-fixed point results in b-metric spaces with applications. Cumhuriyet Science Journal, 40(2), 447-456. https://doi.org/10.17776/csj.421975