Details

Autor(en) / Beteiligte

• Manar, Youssef
• Elqorachi, Elhoucien
• Rassias, Themistocles M.

Titel

On the Generalized Hyers–Ulam Stability of the Pexider Equation on Restricted Domains

Ist Teil von

• Handbook of Functional Equations, 2014, Vol.96, p.279-299

Ort / Verlag

United States: Springer

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Let σ: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $E\longrightarrow E$ \end{document} be an involution of the normed space E and let p, M, d be nonnegative real numbers, such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $0<p<1$ \end{document}. In this chapter, we investigate the Hyers–Ulam–Rassias stability of the Pexider functional equations\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{aligned} f(x+y) = &\, g(x)+h(y),\ f(x+y)+g(x-y)=h(x)+k(y),\\ & f(x+y)+g(x+\sigma(y))=h(x)+k(y), x,y\in{E}\end{aligned}$$ \end{document} on restricted domains \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{B}=\{(x,y)\in{E^{2}}: \|x\|^{p}+\|y\|^{p}\geq M^{p}\}$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{C}=\{(x,y)\in{E}^{2}:\|x\|\geq d\; or\; \|y\|\geq d\}.$ \end{document}