The issue of Ulam's type stability of an equation is understood in the following way: when a
mapping which satisfies the equation approximately (in some sense), it is" close" to a …

In this survey we show how various notions of orthogonality appear in the theory of
functional equations. After introducing some orthogonality relations, we give examples of …

We study the conditional functional equation: γ (x+ y)= γ (x− y)⇒ f (x+ y)= f (x) f (y), with a
given function γ; if γ is a norm in a real linear space, then the equation becomes the well …

Let R be the set of real numbers, Y a Banach space and f: R→ Y. We prove the Hyers–Ulam
stability theorem for the quadratic functional inequality‖ f (x+ y)+ f (x− y)− 2 f (x)− 2 f (y)‖≤ …

This paper examines various aspects related to the Cauchy functional equation f (x+ y)= f
(x)+ f (y) f (x+ y)= f (x)+ f (y), a fundamental equation in the theory of functional equations. In …

We solve conditional Pexider functional equations on prescribed sets being generalizations
of spheres, or defined for vectors satisfying a generalized James orthogonality condition …

In this paper, we prove the Hyers-Ulam stability theorem when $${f, g, h:\mathbb
{R}\to\mathbb {R}} $$ satisfy in a set $${\Gamma\subset\mathbb {R}^{2}} $$ of measure …

We study the exponential functional equation f (x+ y)= f (x) f (y) for (x; y)∈ D⊂ X× X, where X
is the domain of f. Regardless of the solutions of this equation, which in many special cases …

This volume covers the topic in functional equations in a broad sense and is written by
authors who are in this field for the past 50 years. It contains the basic notions of functional …

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