Common Fixed Point Results for w-α-Distance

Year 2024, Volume: 12 Issue: 1, 7 - 11, 01.07.2024

Gülcan Atıci Turan , Fatma Polat

https://doi.org/10.18586/msufbd.1367657

Abstract

In this study, we examined some fixed point theorems in non-full metric spaces. We define the notions of α-lower semi-continuous , w-α-distance, w_0-α– distance, w-α-rational contraction and generalized w-α-rational contraction mapping. We also give related theorem and example. Then, we prove Banach’s fixed-point theorem thanks to the concept w-α- distance in metric spaces equipped with an abritrary binary relation. Also, w-α- rational contraction mapping and generalized w-α-rational contraction mapping are defined and by using these definitions, the theorem related fixed point is expressed and proved.

Keywords

Binary Relation, Fixed Point, α-Complete Metric Space, w-Distance.

Common Fixed Point Results for w-α-distance

Abstract

Bu çalışmada, tam olmayan metrik uzaylarda bazı sabit nokta teoremlerini inceledik. Alt yarı-sürekli, --uzaklık, --uzaklık, --rasyonel daralma ve genelleştirilmiş --rasyonel daralma eşlemesi kavramlarını tanımladık. Ayrıca ilgili teoremi ve örneği veriyoruz. Daha sonra, Banach'ın sabit nokta teoremini metrik uzaylarda - - uzaklık kavramı sayesinde ispatlıyoruz. Ayrıca - - rasyonel daralma haritalaması ve genelleştirilmiş - - rasyonel daralma haritalaması tanımlanmış ve bu tanımlar kullanılarak sabit nokta ile ilgili teorem ifade edilmiş ve ispatlanmıştır.

Keywords

İkili bağıntı, Sabit nokta, α-tam metrik uzay, w-mesafe

References

• [1] Kada, O., Suzuki, T., Takahashi, W. Nonconvex minimization theorems and fixed point theorems in complete metriz spaces, Mathematica Japonica. 44:2 381-391, 1996.
• [2] Samet, B., Vetro, C., Vetro, P. Fixed point theorems - -conractive type mappings, Nonlinear Analysis: Theory, Methods and Applications. 75:4 2154- 2165, 2012.
• [3] Hussain, N., Kutbi, M. A., Salimi, P. Fixed point theory in -complete metric spaces with applications, Abstract and Applied Analysis. 1:2 1-11, 2014.
• [4] Kutbi, M. A., Sintunavarat, W. The existence of fixed point theorems via -distance and -admissible mappings and applications, Abstract and Applied Analysis. 141 1-8, 2013.
• [5] Vetro, C. A Fixed-Point Problem with Mixed-Type Contractive Condition, Constructıve Mathematıcal Analysıs. 3:1, 45-52, 2020.
• [6] Karapinar, E. A Short Survey on the Recent Fixed Point Results on b-Metric Spaces, Constructıve Mathematıcal Analysıs. 1:1 15-44, 2018.
• [7] Nazam, M., Acar, Ö. Fixed points of (α,ψ)‐contractions in Hausdorff partial metric spaces, Mathematical Methods in the Applied Sciences. 42:16 5159-5173, 2019.
• [8] Mınak, G., Acar, Ö.,Altun, İ.. Multivalued Pseudo-Picard Operators and Fixed Point Results, Journal of Function spaces and applications. 2013, 2013.
• [9] Kutbi, M. A., Sintunavarat, W. Fixed point theorems for generalized - contraction multivalued mappings in -complete metric spaces, Fixed Point Theory and Applications. 139 1-9, 2014.