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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 5

FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES

Sun Young JANG
Choonkil PARK
Pages
711–723
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al.
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Key Findings & Data:Rassias introduced the following equality Xm i,j=1 kxi − xjk 2 = 2m Xm i=1 kxik 2 , Xm i=1 xi = 0, for a fixed integer m ≥ 3.
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Conclusion & Impact:In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fuzzy Banach space · Functional equation related to inner product space · Generalized Hyers-Ulam stability

Abstract

The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Th. M. Rassias introduced the following equality Xm i,j=1 kxi − xjk 2 = 2m Xm i=1 kxik 2 , Xm i=1 xi = 0, for a fixed integer m ≥ 3. By the above equality, we define the following functional equation(0.1) Xm i,j=1 f(xi − xj ) = 2m Xmi=1 f(xi), Xm i=1 xi = 0. In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

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Cite This Article

JANG, S. Y., PARK, C. (2022). FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 5, 711–723. https://ajindex.com/articles/530554

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