Common Fixed Point Results for a Class of (𝜶,𝜷)−Geraghty Contraction Type Mappings in Modular Metric Spaces

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 150 - 161, 28.02.2020

Merve Aktay

https://doi.org/10.18185/erzifbed.621292

Cited By: 1

Abstract

Bu makalede 𝛼− Geraghty daraltan tipi dönüşümlerin sınıfından daha zayıf olan (𝛼,𝛽)−uygun çifti aracılığıyla genelleştirilmiş (𝛼,𝛽)− Geraghty daraltan tipi dönüşüm kavramı Modüler metrik uzaylarda tanıtıldı. Bu tarz dönüşümler için bazı sabit nokta ve periyodik nokta sonuçları verildi. Sonuç olarak elde edilen sonuçlar Banach daraltan ilkesinin çeşitli genelleştirmelerini kapsar.

Keywords

Sabit nokta, modüler metrik, Geraghty daraltan dönüşümler

Common Fixed Point Results for a Class of (α,β)-Geraghty Contraction Type Mappings in Modular Metric Spaces

Abstract

Bu makalede  a- Geraghty daraltan
tipi dönüşümlerin sınıfından daha zayıf olan uygun
çifti aracılığıyla genelleştirilmiş a- Geraghty daraltan
tipi dönüşüm kavramı Modüler
metrik uzaylarda tanıtıldı.
Bu tarz dönüşümler için bazı sabit nokta ve periyodik nokta sonuçları verildi.
Sonuç olarak elde edilen sonuçlar Banach daraltan ilkesinin çeşitli
genelleştirmelerini kapsar.

Keywords

Sabit nokta, modüler metrik, Geraghty contraction maps

References

• [1] Amini-Harandi, A. and Emani, H. 2010. “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations”, Nonlinear Anal., 72, 2238–2242. doi:10.1016/j.na. 2009.10.023.[2] Arshad, M., Hussain, A. and Azam, A. 2016. “Fixed point of α-Geraghty contraction with applications”, U.P.B. Sci. Bull., Series A, 78-2.[3] Aydi, H. 2015. “α-implicit contractive pair of mappings on quasi b-metric spaces and application to integral equations”, Accepted in J. Nonlinear Convex Anal.[4] Azadifar, B., Maramaei, M. and Sadeghi, G. 2013. “On the modular G-metric spaces and fixed point theorems”, J. Nonlinear Sci. Appl., 6(4), 293-304.[5] Banach, S. 1922. “Sur les opérationes dans les ensembles abstraits et leur application aux équation intégrales”, Fundam. Math., 3, 133-181.[6] Caballero, J., Harjani, J. and Sadarangani, K. 2012. “A best proximity point theorem for Geraghty-contractions” Fixed Point Theory Appl., Article ID 231.[7] Chaipunya, P., Cho, YE. and Kumam, P. 2012. “Geraghty-type theorems in modular metric spaces with an application to partial differential equation”, Adv. Differ. Equ., Article ID 83.[8] Chaipunya, P., Mongkolkeha, C., Sintunavarat, W. and Kumam, P. 2012. “Fixed-point theorems for multivalued mappings in modular metric spaces”, Abstr Appl Anal., 14, Article ID 503504.[9] Chandok, S. 2015. “Some fixed point theorems for (α,β)-admissible Geraghty type contractive mappings and related results”, Math. Sci., 9, 127–13, doi: 10.1007/s40096-015-0159-4.S.[10] Chistyakov, VV. 2010. “Modular metric spaces, I: basic concepts”, Nonlinear Anal., 72, 1–14, doi:10.1016/j.na.2009.04.057.[11] Chistyakov, VV. 2011. “A fixed point theorem for contractions in modular metric spaces”, Perprint submited to arxiv.[12] Cho, SH., Bae, JS. and Karapınar, E. 2013. “Fixed point theorems for α-Geraghty contraction type maps in metric spaces”, Fixed Point Theory Appl., Article ID 329.[13] Geraghty, M. 1973. “On contractive mappings”, Proc Am Math Soc., 40, 604–608, doi:10.1090/S0002-9939-1973-0334176-5.[14] Eshaghi Gordji, M., Ramezani, M., Cho, YJ. and Pirbavafa, S. 2012. “A generalization of Geraghty’s theorem in partially ordered metric spaces and application to ordinary differential equations”, Fixed Point Theory Appl., 74.[15] Hussain, N., Latif, A. and Iqbal, I. 2015. “Fixed point results for generalized F-contractions in modular metric and fuzzy metric spaces”, Fixed Point Theory Appl., 158.[16] Jeong, G S. and Rhoades B E. 2005. “Maps for which F(T)=F(T^n)”, Fixed Point Theory Appl., 6, 87–131.[17] Karapınar, E. and Samet, B. 2014. “Note on ‘ψ-Geraghty type contractions’”, Fixed Point Theory Appl., Article ID 26.[18] Kuaket, K. and Kumam, P. 2011. “Fixed point for asymptotic pointwise contractions in modular space”, Appl. Math. Lett., 24, 1795-1798.[19] Kumam, P. 2004. “Some geometric properties and fixed point theorem in modular spaces”, In: Garcia Falset J, Fuster L, Sims B (eds.) Fixed Point Theorem and its Applications, Yokohama Publishers, Yokohama, 173–188.[20] Mongkolkeha, C., Sintunavarat, W. and Kumam, P. 2011. “Fixed point theorems for contraction mappings in modular metric spaces”, Fixed Point Theory Appl., 93, doi:10.1186/1687-1812-2011-93165H.[21] Mongkolkeha, C., Cho, YE. And Kumam, P. 2013. “Best proximity points for Geraghty’s proximal contraction mappings”, Fixed Point Theory Appl., Article ID 180.[22] Padcharoen, A., Gopal, D., Chaipunya, P. and Kumam, P. 2016. “Fixed point and periodic point results for α-type F-contractions in modular metric spaces”, Fixed Point Theory and Applications, 39, DOI 10.1186/s13663-016-0525-4R.[23] Samet, B., Vetro, C. and Vetro, P. 2012. “Fixed point theorems for α-ψ-contractive mappings”, Nonlinear Anal., 75, 2154-2165.