In this paper, we discuss some properties of generalized modular metric spaces. This space was first introduced by Turkoglu and Manav in 2018. Later, we extend the concepts about contraction mappings in generalized modular metric spaces. We also develop a convexity structure and defined the N normal structure in this space.The results show us that if X is a complete modular metric space and TN is a contraction mapping then T has a unique fixed point.Moreover, we need the constant of generalized modular metric axiom should be less than or equal to 1 to guarantee the ball is closed. The closeness property of the ball is necessary to generate normal structure in generalized modular metric space. This normal structure property assures the existence of the fixed point of a nonexpansive mapping.
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8 December 2022
PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON INNOVATION IN MATHEMATICS AND MATHEMATICS EDUCATION (ISIMMED) 2020: Rethinking the role of statistics, mathematics and mathematics education in society 5.0: Theory, research, and practice
15 October 2020
Yogyakarta, Indonesia
Research Article|
December 08 2022
Some fixed point theorems in generalized modular metric space
L Harini;
L Harini
a)
Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta
, Yogyakarta, Indonesia
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H. P. Lestari;
H. P. Lestari
Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta
, Yogyakarta, Indonesia
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Caturiyati
Caturiyati
Mathematics Education, Faculty of Mathematics and Natural Sciences, Universitas Negeri Yogyakarta
, Yogyakarta, Indonesia
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AIP Conf. Proc. 2575, 060003 (2022)
Citation
L Harini, H. P. Lestari, Caturiyati; Some fixed point theorems in generalized modular metric space. AIP Conf. Proc. 8 December 2022; 2575 (1): 060003. https://doi.org/10.1063/5.0107775
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