On Intuitionistic Fuzzy n-Controlled Metric Spaces with Application in Economics

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DOI: https://doi.org/10.28924/2291-8639-22-2024-225
Published: Dec 9, 2024
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Lifang Guo, Babar Ali, Abeer Alshejari, Tayyab Kamran, Umar Ishtiaq, On Intuitionistic Fuzzy n-Controlled Metric Spaces with Application in Economics, Int. J. Anal. Appl., 22 (2024), 225.

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Lifang Guo, Babar Ali, Abeer Alshejari, Tayyab Kamran, Umar Ishtiaq

Abstract

In this paper, we introduce the concept of an intuitionistic fuzzy n-controlled metric space (IFnCMS) by using \(n\) non-comparable functions \(\alpha_{i}:\Sigma\times\Sigma\rightarrow[1,\infty)\) \(\text{(1\(\leq i\leq n\))}\) in the inequalities having the form \(F(\varsigma^{o}_{1},\varsigma^{o}_{n+1},\iota^{o}_{1}+\iota^{o}_{2}+\dots+\iota^{o}_{n})\geq F\left(\varsigma^{o}_{1},\varsigma^{o}_{2},\frac{\iota^{o}_{1}}{\alpha_{1}(\varsigma^{o}_{1},\varsigma^{o}_{2})}\right)\) \(\ast F\left(\varsigma^{o}_{2},\varsigma^{o}_{3},\frac{\iota^{o}_{2}}{\alpha_{2}(\varsigma^{o}_{2},\varsigma^{o}_{3})}\right) \ast \dots \ast F\left(\varsigma^{o}_{n},\varsigma^{o}_{n+1},\frac{\iota^{o}_{n}}{\alpha_{n}(\varsigma^{o}_{n},\varsigma^{o}_{n+1})}\right)\) \(\text{for all } \iota^{o}_{n}>0\) and \(N(\varsigma^{o}_{1},\varsigma^{o}_{n+1},\iota^{o}_{1}+\iota^{o}_{2}+\dots+\iota^{o}_{n})\leq N\left(\varsigma^{o}_{1},\varsigma^{o}_{2},\frac{\iota^{o}_{1}}{\alpha_{1}(\varsigma^{o}_{1},\varsigma^{o}_{2})}\right)\) \(\circ N\left(\varsigma^{o}_{2},\varsigma^{o}_{3},\frac{\iota^{o}_{2}}{\alpha_{2}(\varsigma^{o}_{2},\varsigma^{o}_{3})}\right) \circ \dots \circ N\left(\varsigma^{o}_{n},\varsigma^{o}_{n+1},\frac{\iota^{o}_{n}}{\alpha_{n}(\varsigma^{o}_{n},\varsigma^{o}_{n+1})}\right)\) \(\text{for all } \iota^{o}_{n}>0\). Further, we provide some non-trivial examples and prove several fixed point results by utilizing an intuitionistic fuzzy version of Banach contraction and generalized \(\alpha-\phi-\)intuitionistic fuzzy contractive mapping in the setting of IFnCMS. Furthermore, we present some of its consequences to illustrate the significance of our results. Ultimately, we apply fractional differential equations used in economics to support the main result.

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