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ISSN : 1226-0657

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Vol.23 No.2

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ADDITIVE ρ-FUNCTIONAL INEQUALITIES

Additive -functional inequalities

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.2, pp.155-162
https://doi.org/10.7468/jksmeb.2016.23.2.155
LEE, SUNG JIN (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
LEE, JUNG RYE (DEPARTMENT OF MATHEMATICS, DAEJIN UNIVERSITY)
SEO, JEONG PIL (OHSANG HIGH SCHOOL)
LEE, SUNG JIN, LEE, JUNG RYE, & SEO, JEONG PIL. (2016). ADDITIVE ρ-FUNCTIONAL INEQUALITIES. 한국수학교육학회지시리즈B:순수및응용수학, 23(2), 155-162, https://doi.org/10.7468/jksmeb.2016.23.2.155

Abstract

In this paper, we solve the additive &#x3C1;-functional inequalities (0.1)<TEX>${\parallel}f(x+y)+f(x-y)-2f(x){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$</TEX>, where &#x3C1; is a fixed complex number with |&#x3C1;| &#x3C; 1, and (0.2) <TEX>${\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}$</TEX>, where &#x3C1; is a fixed complex number with |&#x3C1;| &#x3C; 1. Furthermore, we prove the Hyers-Ulam stability of the additive &#x3C1;-functional inequalities (0.1) and (0.2) in complex Banach spaces.

keywords
Hyers-Ulam stability, additive ρ-functional inequality

참고문헌

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한국수학교육학회지시리즈B:순수및응용수학

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