peer reviewedThe invariance identity involving three operations D_{f,g} : X x X -> X of the form D_{f,g} (x,y) = (f o g)^{-1} (f (x) + g (y)) , is proposed. The connections of these operations with means is investigated. The question when the invariance equality admits three means leads to a com- posite functional equation. Problem to determine its continuous solutions is pose
We observe that bisymmetry is in fact the assertion of the Fubini theorem and we describe the form ...
AbstractFor a function f defined in an interval I, satisfying the conditions ensuring the existence ...
AbstractOur aim is to solve the so-called invariance equation in the class of two-variable Gini mean...
The invariance identity involving three operations D_{f,g} : X x X -> X of the form D_{f,g} (x,y) = ...
Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The ope...
AbstractIn this paper, we study the invariance of the geometric mean with respect to some generalize...
AbstractThe aim of this paper is to find those pairs of generalized quasi-arithmetic means on an ope...
AbstractThe invariance of the geometric mean G with respect to the Cauchy mean-type mapping (Df,g,Dh...
AbstractLet a positive integer k≥2 and an interval I⊂R be fixed. For a continuous strictly monotonic...
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uni...
Given two functions f, g : I -> R and a probability measure mu on the Borel subsets of [0, 1], the t...
We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \c...
We prove that whenever the selfmapping $(M_1,\dots,M_p)\colon I^p \to I^p$, ($p \in \mathbb{N}$ and ...
AbstractWe determine the class of all pairs of the Lagrangian means forming mean-type mappings which...
AbstractLet I⊂R be a non-trivial interval and let λ,μ,ν:I2→(0,1). We present some results concerning...
We observe that bisymmetry is in fact the assertion of the Fubini theorem and we describe the form ...
AbstractFor a function f defined in an interval I, satisfying the conditions ensuring the existence ...
AbstractOur aim is to solve the so-called invariance equation in the class of two-variable Gini mean...
The invariance identity involving three operations D_{f,g} : X x X -> X of the form D_{f,g} (x,y) = ...
Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The ope...
AbstractIn this paper, we study the invariance of the geometric mean with respect to some generalize...
AbstractThe aim of this paper is to find those pairs of generalized quasi-arithmetic means on an ope...
AbstractThe invariance of the geometric mean G with respect to the Cauchy mean-type mapping (Df,g,Dh...
AbstractLet a positive integer k≥2 and an interval I⊂R be fixed. For a continuous strictly monotonic...
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uni...
Given two functions f, g : I -> R and a probability measure mu on the Borel subsets of [0, 1], the t...
We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \c...
We prove that whenever the selfmapping $(M_1,\dots,M_p)\colon I^p \to I^p$, ($p \in \mathbb{N}$ and ...
AbstractWe determine the class of all pairs of the Lagrangian means forming mean-type mappings which...
AbstractLet I⊂R be a non-trivial interval and let λ,μ,ν:I2→(0,1). We present some results concerning...
We observe that bisymmetry is in fact the assertion of the Fubini theorem and we describe the form ...
AbstractFor a function f defined in an interval I, satisfying the conditions ensuring the existence ...
AbstractOur aim is to solve the so-called invariance equation in the class of two-variable Gini mean...
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