(𝓕,𝒉) Üst Sınıfı Aracılığıyla (𝝍,𝝋) Zayıf Büzülme Dönüşümleri Üzerine Bir Çalışma

Year 2023, , 2057 - 2067, 01.09.2023

Esra Yolacan

https://doi.org/10.21597/jist.1251523

Abstract

Branciari, metrik uzaydaki iki terimli üçgen eşitsizliğini üç terimli dörtgen eşitsizliğiyle yer değiştirerek yeni bir mesafe fonksiyonu oluşturmak için metrik kavramını yeniden yapılandırdı. Tanımlanan bu fonksiyon literatürde dikdörtgensel metrik ya da genelleştirilmiş metrik olarak adlandırılır. Ansari tarafından ortaya konulan üst sınıf dönüşümü temel alınarak Branciari metrik uzayında üst sınıf tip II aracılığıyla zayıf büzülmeli dönüşümlerin bir genellemesi verildi. Sonraki aşamada ise bir çizge vasıtasıyla Branciari metrik uzayında grafik zayıf büzülmeli dönüşümler için yeni sabit nokta sonuçlarını ispat etmek amacıyla burada bir uygulama verildi. Son olarak çalışılan dönüşüm için ana sonuçlarımızı destekleyen bir örnek gösterildi.

Keywords

sabit nokta, Branciari metrik uzayı, (F,h) Üst Sınıfı

Supporting Institution

-

Project Number

-

Thanks

-

A Study on (𝝍,𝝋) Weakly Contractive Mapping via (𝓕,𝒉) Upper Class

Abstract

Branciari reorganized the notion of metric to attain a novel distance function by replacing the triangular inequality with the quadrilateral inequality. The reorganized metric function was said rectangular metric in some resources, or general metric in some others. Ansari introduced a more general function so-called upper class. Inspired and motivated by this facts, we give an extansion of weakly contractive mapping via upper class type II in the setting of Branciari metric space. An application is given here to prove new fixed point results for graphic weakly contractive mappings in Branciari metric space endowed with a graph. Moreover, we derive an example in support of our main results.

Keywords

fixed point, Branciari metric space, (F,h) Upper class

Project Number

-

References

• Abagaro, B.N., Tola, K.K., Mamud, M.A. (2022). Fixed point theorems for Generalized (α,ψ)-contraction mappings in Rectangular quasi b-metric space. Fixed Point Theory and Applications, 2022:13.
• Al-Khaleel et al. (2023). On Cyclic Contractive Mappings of Kannan and Chatterjea Type in Generalized Metric Spaces. Mathematics, 11(4), 890.
• Ansari, A.H. (2014). Note on “α-admissible mappings and related fixed point theorems”. The 2nd Regional Conference on Mathematics and Applications, PNU,373-376.
• Ansari, A.H., Abodayeh, K. (2020). Upper class functions on a controlled contraction principle in partial S-metric spaces. Italian Journal of Pure and Applied Mathematics, No 43, 1-13.
• Ansari et al. (2022). A survey of C-class and pair upper-class functions in fixed point theory. The International Journal of Nonlinear Analysis and Applications, 13 (1), 1879-1896.
• Ansari, A.H. and Shukla, S. (2016). Some fixed point theorems for ordered F-(F,h)-contraction and subcontractions in 0-f-orbitally complete partial metric spaces. Journal of Advanced Mathematical Studies, 9(1),37-53.
• Ansari, A. H., Tomar A. (2021). C-class and pair upper class functions and other kind of contractions in fixed point theory. Scientific Publications of The State University of Novi Pazar, 13 (1), 43-60.
• Arshad, M., Ameer, E., Karapınar, E. (2016). Generalized contractions with triangular α-orbital admissible mapping on Branciari metric spaces. Journal of Inequalities and Applications. 2016:63. Doi: 10.1186/s13660-016-1010-7.
• Baiya, S., Kaewcharoen, A. (2019). Fixed point theorems for Generalized contractions with triangular α-orbital admissible mapping on Branciari metric spaces. Thai Journal of Mathematics, 17 (3):703-725.
• Bisht, R.K. (2023). An overview of the emergence of weaker continuity notions, various classes of contractive mappings and related fixed point theorems. Journal of Fixed Point Theory and Applications, 2023:25 (11).
• Branciari, A. (2000). A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces. Publicationes Mathematicae Debrecen, 57 (1):31-37.
• Chiroma et al. (2023). On the Existence of Solutions to a Boundary Value Problem via New Weakly Contractive Operator. Axioms, 12(4), 397.
• Huang, H., Ansari, A.H., Dekic, D.D., Radenovic, S. (2017). Some fixed point results for rational type and subrational type contractive mappings. The Acta Universitatis Sapientiae Mathematica, 9 (1): 185-201.
• Hussain, N., Al-Mezel, S., Salimi, P. (2013). Fixed points for ψ-Graphic contractions with applications to integral equations. Abstract and Applied Analysis, volume 2013, Article ID 575869, 11 pages.
• Jachymski, J. (2008). The contraction principle for mappings on a metric space with a graph. Proceedings of the American Mathematical Society, 136,1359-1373.
• Kadelburg, Z. and Radenovic, S. (2014). Fixed point results in generalized metric spaces without Hausdorff property. Mathematical Sciences, 8:125. Doi: 10.1007/s40096-014-0125-6.
• Karapinar, E., Kumam, P. and Salimi, P.,(2013). On α-ψ-Meir-Keeler contractive mappings. Fixed Point Theory and Applications, 2013:94.
• Li, C., Cui, Y., Chen, L. (2022). Fixed point results on Closed Ball in Convex Rectangular b-metric spaces and applications. Journal of Functional Spaces, Volume 2022, Article ID 8840964.
• Mamud, M.A., Tola, K.K.(2022). Fixed point results for generalized (α,ψ)-contraction mappings in Rectangular b-metric space, Abstract and Applied Analysis, volume 2022, Article ID 9370083, 12 pages.
• Patil, J., Hardan, B., Hamoud, A.A., Bachhav, A., Emadifar, H. (2022). A New result on Branciari metric spaces using (α,γ)-contractive mappings. Topological Algebra and its Applications, 10:103-112.
• Popescu, O. (2014). Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces. Fixed Point Theory and Applications, 2014:190.
• Ruzhansky et al. (2017). Advances in Real and Complex Analysis with Applications. 1 Ed. Springer, 183-241.
• Salimi, P., Latif, A., Hussain N. (2013). Modified α-ψ-contractive mappings with Applications, Fixed Point Theory and Applications, 2013:151.
• Samet, B. (2010). Discussion on “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces” by A.Branciari, Publicationes Mathematicae Debrecen, 76, 493-494.
• Sarma, I.R., Rao, J.M., Rao, S.S. (2009). Contractions over generalized metric spaces. Journal of Nonlinear Sciences and Applications, 2(3), 180-182.
• Yolacan, E. (2016). Some fixed point theorems on generalized metric spaces. Asian Journal of Mathematics and Applications, vol.2016, Article ID ama0294, 8 pages.