Scholarlink

Abstract <p> Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((X,\bot)\)</EquationSource> </InlineEquation> be an orthogonality Banach space in the sense of Rätz and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Y\)</EquationSource> </InlineEquation> be a Banach space. In this paper, we apply the alternative fixed point theorem for proving the Hyers–Ulam stability of the orthogonally generalized additive-quadratic functional equation of the form <Equation ID="Equi"> <EquationSource Format="TEX">\(f(ax+by)+f(ax-by)+2b^2f(y) = (a^2+a)f(x)+(a^2-a)f(-x)+b^2f(2y)\)</EquationSource> </Equation> for all <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(x,y \in X\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(x\bot y\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(a\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(b\)</EquationSource> </InlineEquation> are fixed nonzero rational numbers and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(f\)</EquationSource> </InlineEquation> maps from <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(X\)</EquationSource> </InlineEquation> to <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(Y\)</EquationSource> </InlineEquation>. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On New Orthogonally Generalized Additive-Quadratic Functional Equations in the Sense of Rätz and Their Stability

  • 期刊论文

  • 发表日期：

    2025年8月1日

查看全文
  • L. Aiemsomboon,
  • A. Thanyacharoen,
  • W. Sintunavarat

摘要

Abstract

Let \((X,\bot)\) be an orthogonality Banach space in the sense of Rätz and \(Y\) be a Banach space. In this paper, we apply the alternative fixed point theorem for proving the Hyers–Ulam stability of the orthogonally generalized additive-quadratic functional equation of the form \(f(ax+by)+f(ax-by)+2b^2f(y) = (a^2+a)f(x)+(a^2-a)f(-x)+b^2f(2y)\) for all \(x,y \in X\) with \(x\bot y\) , where \(a\) and \(b\) are fixed nonzero rational numbers and \(f\) maps from \(X\) to \(Y\) .