On one-local retract in modular metrics | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 9، دوره 20، شماره 1، فروردین 2024، صفحه 201-220 اصل مقاله (520.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.2023.234064.1451 | ||
| نویسندگان | ||
| Oliver Olela Otafudu* ؛ Tlotlo Odacious Phawe | ||
| School of Mathematical and Statistical Sciences North-West University, Potchefstroom Campus, Potchefstroom 2520, South Africa. | ||
| چکیده | ||
| We continue the study of the concept of one local retract in the settings of modular metrics. This concept has been studied in metric spaces and quasi-metric spaces by different authors with different motivations. In this article, we extend the well-known results on one-local retract in metric point of view to the framework of modular metrics. In particular, we show that any self-map $\psi: X_w \longrightarrow X_w$ satisfying the property $w(\lambda,\psi(x),\psi(y)) \leq w(\lambda,x,y)$ for all $x,y \in X$ and $\lambda >0$, has at least one fixed point whenever the collection of all $q_w$-admissible subsets of $X_{w}$ is both compact and normal. | ||
| کلیدواژهها | ||
| Fixed point؛ one local retract؛ normal structure؛ $w$-admissible | ||
| مراجع | ||
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[1] Abdou, A.A.N., One-local retract and common fixed point in modular metric spaces, Abstr. Appl. Anal. (2013), Art. ID 67206, 8pp. [2] Chistyakov, V.V., Modular metric spaces, I: Basic concepts, Nonlinear Anal. 72 (2010), 1-14. [3] Chistyakov, V.V., A fixed point theorem for contractions in modular metric spaces, https://arxiv.org/abs/1112.5561 (preprint). [4] Chistyakov, V.V., “Metric Modular Spaces: Theory and Applications”, Springer Briefs in Mathematics, Springer, 2015. [5] Hussain, N., Khamsi, M.A., and Kirk, W.A., One-local retracts and Banach operator pairs in Metric Spaces, Appl. Math. Comput. 218 (2012), 10072-10081. [6] Hussain, N., Jungck, G., and Khamsi, M.A., Nonexpansive retracts and weak compatible pairs in metric spaces, Fixed Point Theory Appl. (2012), Art. No. 100 (2012). [7] Khamsi, M.A., One-local retract and common fixed point for commuting mappings in metric spaces, Nonlinear Anal. 27 (1996), 1307-1313. [8] Khamsi, M.A. and Kirk, W.A., “An Introduction to Metric Spaces and Fixed Point Theory”, John Wiley, 2001. [9] Otafudu, O.O. and Sebogodi, K., On w-Isbell-convexity, Appl. Gen. Topol. 23 (2022), 91-105. [10] Otafudu, O.O., On one-local retract in quasi-metric spaces, Topology Proc. 45 (2015), 271-281. | ||
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