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Volume 15
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Article

Banach Fixed Point Theorems in Generalized Metric Space Endowed with the Hadamard Product

by
Saleh Omran
1,
Ibtisam Masmali
2 and
Ghaliah Alhamzi
3,*
1
Department of Mathematics, South Valley University, Qena 83523, Egypt
2
Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
3
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2023, 15(7), 1325; https://doi.org/10.3390/sym15071325
Submission received: 26 May 2023 / Revised: 26 June 2023 / Accepted: 27 June 2023 / Published: 28 June 2023
(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)
Versions Notes

Abstract

In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to zero is not needed, this produces stronger results than those of Perov. As an application of our results, we study the existence and uniqueness of the solution for a system of matrix equations.
Keywords: Banach fixed point theorems; generalized metric space; Hadamard product Banach fixed point theorems; generalized metric space; Hadamard product

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MDPI and ACS Style

Omran, S.; Masmali, I.; Alhamzi, G. Banach Fixed Point Theorems in Generalized Metric Space Endowed with the Hadamard Product. Symmetry 2023, 15, 1325. https://doi.org/10.3390/sym15071325

AMA Style

Omran S, Masmali I, Alhamzi G. Banach Fixed Point Theorems in Generalized Metric Space Endowed with the Hadamard Product. Symmetry. 2023; 15(7):1325. https://doi.org/10.3390/sym15071325

Chicago/Turabian Style

Omran, Saleh, Ibtisam Masmali, and Ghaliah Alhamzi. 2023. "Banach Fixed Point Theorems in Generalized Metric Space Endowed with the Hadamard Product" Symmetry 15, no. 7: 1325. https://doi.org/10.3390/sym15071325

APA Style

Omran, S., Masmali, I., & Alhamzi, G. (2023). Banach Fixed Point Theorems in Generalized Metric Space Endowed with the Hadamard Product. Symmetry, 15(7), 1325. https://doi.org/10.3390/sym15071325

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