On existence results of Volterra-type integral equations via $ C^* $-algebra-valued $ F $-contractions

Mohammed Shehu Shagari; Trad Alotaibi; OM Kalthum S. K. Mohamed; Arafa O. Mustafa; Awad A. Bakery; Mohammed Shehu Shagari; Trad Alotaibi; OM Kalthum S. K. Mohamed; Arafa O. Mustafa; Awad A. Bakery

doi:10.3934/math.2023058

AIMS Mathematics

2023, Volume 8, Issue 1: 1154-1171. doi: 10.3934/math.2023058

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Research article

On existence results of Volterra-type integral equations via $ C^* $-algebra-valued $ F $-contractions

1.
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
2.
Department of Mathematics, College of Science, Taif University, P. O. BOX 1109, Taif 21944, Saudi Arabia
3.
College of Science and Arts at Khulis, Department of Mathematics, University of Jeddah, Jeddah, Saudi Arabia
4.
Academy of Engineering and Medical Sciences, Department of Mathematics, Khartoum, Sudan
5.
University of Jeddah, College of Business at Khulis, Jeddah, Saudi Arabia
6.
Faculty of Science, Department of Mathematics, Ain Shams University, Cairo, Egypt

Received: 02 September 2022 Revised: 24 September 2022 Accepted: 07 October 2022 Published: 18 October 2022
MSC : 34A12, 47H10, 54H25

It is a fact that $ C^* $-algebra-valued metric space is more general and hence the results in this space are proper improvements of their corresponding ideas in standard metric spaces. With this motivation, this paper focuses on introducing the concepts of $ C^* $-algebra-valued $ F $-contractions and $ C^* $-algebra-valued $ F $-Suzuki contractions and then investigates novel criteria for the existence of fixed points for such mappings. It is observed that the notions examined herein harmonize and refine a number of existing fixed point results in the related literature. A few of these special cases are highlighted and analyzed as some consequences of our main ideas. Nontrivial comparative illustrations are constructed to support the hypotheses and indicate the preeminence of the obtained key concepts. From application viewpoints, one of our results is applied to discuss new conditions for solving a Volterra-type integral equation.
Citation: Mohammed Shehu Shagari, Trad Alotaibi, OM Kalthum S. K. Mohamed, Arafa O. Mustafa, Awad A. Bakery. On existence results of Volterra-type integral equations via $ C^* $-algebra-valued $ F $-contractions[J]. AIMS Mathematics, 2023, 8(1): 1154-1171. doi: 10.3934/math.2023058

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Abstract

It is a fact that $ C^* $-algebra-valued metric space is more general and hence the results in this space are proper improvements of their corresponding ideas in standard metric spaces. With this motivation, this paper focuses on introducing the concepts of $ C^* $-algebra-valued $ F $-contractions and $ C^* $-algebra-valued $ F $-Suzuki contractions and then investigates novel criteria for the existence of fixed points for such mappings. It is observed that the notions examined herein harmonize and refine a number of existing fixed point results in the related literature. A few of these special cases are highlighted and analyzed as some consequences of our main ideas. Nontrivial comparative illustrations are constructed to support the hypotheses and indicate the preeminence of the obtained key concepts. From application viewpoints, one of our results is applied to discuss new conditions for solving a Volterra-type integral equation.

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