ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION
Copyright policy )ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION
Summary: Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation \[ \begin{multlined} f\left(\frac{x}{2}+y\right) + f\left(\frac{x}{2}-y\right) + f\left(\frac{x}{2}+z\right) + f\left(\frac{x}{2}-z\right) \\ = 3f(x) - 1 f (- x) + f(y) + f (- y) + f(z) + f (- z) \end{multlined} \tag{0.1} \] for all \(x,y,z\) with \(x \perp y\), in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.
- Daejin University Korea (Republic of)
- Hanyang University Korea (Republic of)
Systems of functional equations and inequalities, Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory, orthogonally additive and orthogonally quadratic functional equation, Ulam-Hyers stability, Fixed-point theorems, fixed point, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, Functional equations for functions with more general domains and/or ranges, Non-Archimedean analysis, orthogonality space, Special maps on metric spaces, non-Archimedean normed space
Systems of functional equations and inequalities, Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory, orthogonally additive and orthogonally quadratic functional equation, Ulam-Hyers stability, Fixed-point theorems, fixed point, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, Functional equations for functions with more general domains and/or ranges, Non-Archimedean analysis, orthogonality space, Special maps on metric spaces, non-Archimedean normed space
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!