The Uniqueness of Solutions of a System of Functional Equations in Some Classes of Functions.
On the Continuous Dependences of Cr Solutions of a Functional Equation on the Given Functions
A functional inequality characterizing convex functions, conjugacy and a generalization of Hölder's and Minkowski's inequalities.
On Lipschitzian solutions of a functional equation
Correction to the paper "On the continuous dependence of local analytic solutions of a functional equation on given functions''
On the continuous dependence of local analytic solutions of a functional equation on given functions
On the continuous dependence of solutions of a functional equation on given functions
On the continuous dependence of local analytic solutions of the functional equation in the non-uniqueness case
On meromorphic solutions of a functional equation, II
On meromorphic solutions of a functional equation
A fixed point theorem for non-expansive mappings on compact metric spaces.
On the existence of a convex solution of the functional equation φ(x) = h(x,φ[f(x)])
Solutions of a functional equation in a special class of functions
Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities
Let ϕ be an arbitrary bijection of . We prove that if the two-place function is subadditive in then must be a convex homeomorphism of . This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of are also given. We apply the above results to obtain several converses of Minkowski’s inequality.
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]...
On a class of composite functional equations in a single variable.
Local operators and a characterization of the Volterra operator.
Uniformly continuous composition operators in the space of functions of two variables of bounded -variation in the sense of Wiener
Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener -variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable....
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