Some recent applications of functional equations to the social and behavioral sciences. Further problems.
Some regularity properties of algorithms and additive functions with respect to them.
Some remarkable lines of triangles in real normed spaces and characterizations of inner product structures.
Some remarks on a problem of C. Alsina.
Equation[1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y))has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]:[2] f(x+1) + f (f(x)+1) = 1,[3] f(2x) + f(2f(x)) = f(2f(x + f(x))).Equation [3] leads to a Cauchy functional equation:[4] phi(f(x)+x) = phi(f(x)) + phi(x),restricted to the graph of the function f,...
Some remarks on derivations in Banach algebras and related results.
Some remarks on Karmarkar's potential function.
Some remarks on stability and solvability of linear functional equations.
Some remarks on the general theorem of the existence of iterative roots of homeomorphisms with a rational rotation number
We show that the theorem proved in [8] generalises the previous results concerning orientation-preserving iterative roots of homeomorphisms of the circle with a rational rotation number (see [2], [6], [10] and [7]).
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 reproducing identities for families of mean values.
Some results on stability of difference systems.
Some roughness results concerning reducibility for linear difference equations.
Some theorems on differentiable solutions of a system of functional equations of n-th order
Some varieties of groupoids which consist of abelian group or group isotopes.
Spatial discretization of an impulsive Cohen-Grossberg neural network with time-varying and distributed delays and reaction-diffusion terms.
Special solutions of a functional equation
Special solutions of a functional equation
Special solutions of linear difference equations with infinite delay
For the difference equation ,where is a Banach space, is a parameter and is a linear, bounded operator. A sufficient condition for the existence of a unique special solution passing through the point is proved. This special solution converges to the solution of the equation (0) as .
Spectral analysis of unbounded Jacobi operators with oscillating entries
We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the OP family...
Spectral deformations of Jacobi operators.