Quadratic \rho-functional inequalities in \beta-homogeneous normed spaces
Publish Year: 1394
نوع سند: مقاله ژورنالی
زبان: English
View: 95
This Paper With 6 Page And PDF Format Ready To Download
- Certificate
- من نویسنده این مقاله هستم
استخراج به نرم افزارهای پژوهشی:
شناسه ملی سند علمی:
JR_IJNAA-6-2_002
تاریخ نمایه سازی: 11 آذر 1401
Abstract:
In [۱۲], Park introduced the quadratic \rho-functional inequalities\begin{eqnarray}\label{E۰۱}&& \|f(x+y)+f(x-y)-۲f(x)-۲f(y)\| \\ && \qquad \le \left\|\rho\left(۲ f\left(\frac{x+y}{۲}\right) + ۲ f\left(\frac{x-y}{۲}\right)- f(x) - f(y)\right)\right\|, \nonumber\end{eqnarray}where \rho is a fixed complex number with |\rho|<۱,and\begin{eqnarray}\label{E۰۲}&& \left\|۲ f\left(\frac{x+y}{۲}\right) + ۲ f\left(\frac{x-y}{۲}\right)- f(x) - f(y)\right\| \\ && \qquad \le \|\rho(f(x+y)+f(x-y)-۲f(x)-۲f(y))\| , \nonumber\end{eqnarray}where \rho is a fixed complex number with |\rho|<\frac{۱}{۲}.In this paper, we prove the Hyers-Ulam stability of the quadratic \rho-functional inequalities (۰.۱) and (۰.۲) in \beta-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of quadratic \rho-functional equations associated with the quadratic \rho-functional inequalities(۰.۱) and (۰.۲) in \beta-homogeneous complex Banach spaces.
Keywords:
Authors
- -
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul ۱۳۳-۷۹۱, Korea
- -
Department of Mathematics, Hallym University, Chuncheon ۲۰۰-۷۰۲۱, Korea
- -
Department of Mathematics, Daejin University, Kyeonggi ۴۸۷-۷۱۱, Korea
- -
Department of Mathematics, University of Seoul, Seoul ۱۳۰-۷۴۳, Korea