Some inequalities connected with the exponential function
The paper is devoted to some functional inequalities related to the exponential mapping.
Some logarithmic functional equations
The functional equation is solved for general solution. The result is then applied to show that the three functional equations , and are equivalent. Finally, twice differentiable solution functions of the functional equation are determined.
Some models of geometries and a functional equation
Some models of plane geometries and a functional equation
Some monotonicity properties and characterizations of the gamma function.
Some new functional equations connected with characterization problems.
Some new inequalities for the gamma, beta and zeta functions.
Some properties of the jacobian sn z function.
Using some results of the theory of functional equations we deduce some properties of the Jacobian sn z function which seem to be new. Some functional equations have also been found which are fulfilled by the sn z function which the author did not find in the literature.
Some propositions related to a dilation theorem of W. Benz.
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 theorems on differentiable solutions of a system of functional equations of n-th order