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Solvability of functional quadratic integral equations with perturbation

Metwali M. A. M.

Opuscula Mathematica

2013

Vol. 33, no. 4

725--739

We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness.

The superposition operator for vector-valued functions on a noncompact interval

Dronka J., Olszowy L.

Demonstratio Mathematica

2006

Vol. 39, nr 2

411-418

In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a noncompact interval is considered. Acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation in this space is obtained.

Boundedness of superposition operators on some sequence spaces defined by moduli

Molder A.

Demonstratio Mathematica

2006

Vol. 39, nr 4

869-886

For a solid sequence space lambda and a sequence of modulus functions fi = (phik) let lambda(fi) = {x = (xk) : (phik(|xk|)) is an element of lambda}. Provided another solid sequence space ž and a sequence of modulus functions psi= psi(k), we give necessary and sufficient conditions for the local boundedness and boundedness of superposition operators Pf from lambda(fi)) into ž(psi) for some Banach sequence spaces lambda and ž under the assumptions that topologies on the sequence spaces lambda(fi) and ž(psi) are given by certain F-norms. As applications we characterize bounded superposition operators on some multiplier sequence spaces of Maddox type.

Lipschitzian superposition operators between spaces of functions of bounded generalized variation with weight

Chistyakov V. V.

Journal of Applied Analysis

2000

Vol. 6, nr 2

173-186

We present some properties of real valued functions of bounded generalized variation of Riesz-Orlicz type including weight and characterize Lipschitzian superposition Nemytskii operators which map between spaces (in fact, Banach algebras) of these functions.