Solutions and stability of generalized mixed type QC functional equations in random normed spaces.
Solutions of .
Solutions with big graph of iterative functional equations of the first order
We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,𝜑(x),𝜑(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution 𝜑 has some strange properties: it is dense and connected, has full outer measure and is topologically big.
Solutions with big graph of iterative functional equations of higher orders
Solvability of the functional equation f = (T-I)h for vector-valued functions
Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and in measure for some f ∈ M(μ;X), then also in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying...
Some higher order complex vector functional equations
In the present paper some complex vector functional equations of higher order without parameters and with complex parameters are solved.
Some propositions related to a dilation theorem of W. Benz.
Some remarkable lines of triangles in real normed spaces and characterizations of inner product structures.
Some remarks on derivations in Banach algebras and related results.
Some remarks on stability and solvability of linear functional equations.
Some remarks on the stability of the multi-Jensen equation
First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in...
Some varieties of groupoids which consist of abelian group or group isotopes.
Stability and superstability of ring homomorphisms on non-archimedean Banach algebras.
Stability of a 2-dimensional functional equation in a class of vector variable functions.
Stability of a bi-Jensen functional equation. II.
Stability of a Cauchy-Jensen functional equation in quasi-Banach spaces.
Stability of a functional equation coming from the characterization of the absolute value of additive functions.
Stability of a functional equation related to distance measure. II.
Stability of a generalization of the Fréchet functional equation
We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.
Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in -algebras.