Fundamental equation of information revisited.
Generalized sine equations, I.
Generalized sine equations, I. (Summary).
Generalized sine equations, II.
Generalized sine equations, II. (Summary).
Generalized sine equations, III.
Geometrical convexity and generalizations of the Bohr-Mollerup theorem on the gamma function.
Homogeneous means and some functional equations
Hyers-Ulam stability of a bi-Jensen functional equation on a punctured domain.
Hyers-ulam Stability of a General Quadratic Functional Equation
Hyers-Ulam stability of a polynomial equation.
Hyers-Ulam stability of Butler-Rassias functional equation.
Hyers-Ulam stability of functional equations in several variables.
Hyers-Ulam stability of mean value points.
Hyers-Ulam-Rassias stability of the Apollonius type quadratic mapping in RN-spaces.
Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities
The connection between the functional inequalities and is investigated, where D is a convex subset of a linear space, f: D → ℝ, α H;α J: D-D → ℝ are even functions, λ ∈ [0; 1], and ρ: [0; 1] →ℝ+ is an integrable nonnegative function with ∫01 ρ(t) dt = 1.
Invariance identity in the class of generalized quasiarithmetic means
An invariance formula in the class of generalized p-variable quasiarithmetic means is provided. An effective form of the limit of the sequence of iterates of mean-type mappings of this type is given. An application to determining functions which are invariant with respect to generalized quasiarithmetic mean-type mappings is presented.
Invariance in the class of weighted quasi-arithmetic means
Under the assumption of twice continuous differentiability of some of the functions involved we determine all the weighted quasi-arithmetic means M,N,K such that K is (M,N)-invariant, that is, K∘(M,N) = K. Some applications to iteration theory and functional equations are presented.
Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means.
Invariant graphs of functions for the mean-type mappings
Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, ... , Mp : Ip → I the continuous means. We consider the problem of invariance of the graphs of functions ϕ : Jp−1 → I with respect to the mean-type mapping M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean [7], we prove that if the graph of a continuous function ϕ : Jp−1 → I ...