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Stability of ๐‘ -ยญvariable Additive and ๐‘™-ยญvariable Quadratic Functional Equations

Sandra Pinelas|์ด์ •๋ก€|Vediyappan Govindan
ํ•œ๊ตญ์ˆ˜ํ•™๊ต์œกํ•™ํšŒ|2022.05|์ด๋ก ์ˆ˜ํ•™๊ณผ ๊ต์ง์ˆ˜ํ•™ (Theoretical Mathematics and Pedagogical Mathematics)|์ œ29๊ถŒ ์ œ2ํ˜ธ|pp. 179-188|DOI https://doi.org/10.7468/jksmeb.2022.29.2.179

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์ฐธ๊ณ ๋ฌธํ—Œ

ํ‚ค์›Œ๋“œ

Hyers-Ulam stabilityadditive and quadratic mappingquasi-Banach spacep-Banach space
์ฃผ์ œ๋ถ„๋ฅ˜์ˆ˜ํ•™

์ดˆ๋ก

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and ๐‘™-variable quadratic functional equations of the form f(sum _{i=1} ^{s}{x}{i})+ sum _{j=1} ^{s}{f}(-{s}{x}{j}+sum _{i=1,iโ‰ j} ^{s}{x}{i})=0 and f( sum _{i=1} ^{l} {x}{i} )+ sum _{j=1} ^{l} f(-{l}{x}{j}+ sum _{i=1,i != j} ^{l} {x}{i})=(l+1) sum _{i=1,i != j} ^{l} f({x}{i} -{x}{j})+(l+1) sum _{i=1} ^{l} f({x}{i}) (s, ๐‘™โˆˆN, s, ๐‘™โ‰ฅ3)in qusai-Banach spaces.

Abstract

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and ๐‘™-variable quadratic functional equations of the form f(sum _{i=1} ^{s}{x}{i})+ sum _{j=1} ^{s}{f}(-{s}{x}{j}+sum _{i=1,iโ‰ j} ^{s}{x}{i})=0 and f( sum _{i=1} ^{l} {x}{i} )+ sum _{j=1} ^{l} f(-{l}{x}{j}+ sum _{i=1,i != j} ^{l} {x}{i})=(l+1) sum _{i=1,i != j} ^{l} f({x}{i} -{x}{j})+(l+1) sum _{i=1} ^{l} f({x}{i}) (s, ๐‘™โˆˆN, s, ๐‘™โ‰ฅ3)in qusai-Banach spaces.

์ฐธ๊ณ ๋ฌธํ—Œ (18)

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