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Open AccessArticle

Common Fixed Points Results on Non-Archimedean Metric Modular Spaces

by Wissam Kassab 1,2
1
Department of Mathematics and Computer Science, University Politehnica of Bucharest, 060042 Bucharest, Romania
2
Department of Mathematics, International University of Beirut, Mouseitbeh Mazraa 1105, Beirut, Lebanon
Symmetry 2019, 11(11), 1355; https://doi.org/10.3390/sym11111355
Received: 2 September 2019 / Revised: 28 October 2019 / Accepted: 30 October 2019 / Published: 2 November 2019
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
This paper introduces two new contractive conditions in the setting of non-Archimedean modular spaces, via a C-class function, an altering distance function, and a control function. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. The main outcomes provide sufficient conditions for the existence of common fixed points for four mappings. Examples are provided in order to prove the usability of the theoretical approach. Moreover, these examples use a non-Archimedean metric modular, which is not convex, making the study of nonconvex modulars more appealing. View Full-Text
Keywords: non-Archimedean metric modular; common fixed point; C-class function; weak annihilator non-Archimedean metric modular; common fixed point; C-class function; weak annihilator
MDPI and ACS Style

Kassab, W. Common Fixed Points Results on Non-Archimedean Metric Modular Spaces. Symmetry 2019, 11, 1355.

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