Decision making on the mappings' ideal solution of a fuzzy non-linear matrix system of Kannan-type

Volume 30, Issue 1, pp 48--66 https://doi.org/10.22436/jmcs.030.01.06

Publication Date: November 25, 2022 Submission Date: August 17, 2022 Revision Date: September 23, 2022 Accteptance Date: September 27, 2022

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Authors

A. O. Mustafa - University of Jeddah, College of Business at Khulis, Jeddah, Saudi Arabia. - Wadi Al-Neel University, Faculty of Economics and Administrative Sciences, Sudan. A. A. Bakery - University of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi Arabia. - Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Abbassia, Egypt.

Abstract

Since proving many fixed point theorems in a given space requires either growing the space itself or growing the self-mapping that works on it, both of these options are good. The operators' ideal generated by a weighted binomial matrix in the Nakano sequence space of extended s-fuzzy functions is constructed. Some structures for it based on geometry and topology are presented. It has been proven that the Kannan contraction operator has a unique fixed point in this class. Lastly, sufficient conditions such that a fuzzy non-linear matrix system of Kannan-type has a unique solution in this ideal class are investigated and a numerical example to explain our results are given.

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Keywords

• Binomial matrix
• Nakano sequence space
• extended \(s\)-fuzzy functions
• multiplication mapping
• Kannan contraction mapping

MSC

•  46B10
•  46C05
•  46E15

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