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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 23(2), 155-162, https://doi.org/10.7468/jksmeb.2016.23.2.155

Abstract

In this paper, we solve the additive ρ-functional inequalities (0.1)${\parallel}f(x+y)+f(x-y)-2f(x){\parallel}$ $\leq$ ${\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ${\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$ $\leq$ ${\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}$, where ρ is a fixed complex number with |ρ| < 1. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-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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