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The solvability of functional quadratic volterra-urysohn integral equations on the half line

Metwali M. M. A.

Fasciculi Mathematici

2018

Nr 61

109--123

We study the solvability of general quadratic Volterra integral equations in the space of Lebesgue integrable functions on the half line. Using the conjunction of the technique of measures of weak noncompactness with modified Schauder fixed point principle we show that the integral equation, under certain conditions, has at least one solution. Moreover, that result generalizes several ones obtained earlier in many research papers and monographs.

Uniformly continuous superposition operators in the space of functions of bounded n-dimensional Φ-variation

Bracamonte M., Ereú J., Giménez J., Merentes N.

Demonstratio Mathematica

2014

Vol. 47, nr 1

56--68

We prove that if a superposition operator maps a subset of the space of all metric-vector-space-valued-functions of bounded n-dimensional Φ-variation into another such space, and is uniformly continuous, then the generating function of the operator is an affine function in the functional variable.

Superposition Operators in the Space of Functions of Waterman-Shiba Bounded Variation

Giménez J., Merentes N., Rodriguez L.

Commentationes Mathematicae

2014

Vol 54, No. 1

79--93

In this paper we present a necessary condition for an autonomous superposition operator to act in the space of functions of Waterman-Shiba bounded variation. We also show that if a (general) superposition operator applies such space into itself and it is uniformly bounded, then its generating function satisfies a weak Matkowski condition.

On some properties of the superposition operator on topological manifolds

Dronka J.

Opuscula Mathematica

2010

Vol. 30, no. 1

69-77

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

Superposition operators on sequence spaces defined by (phi)-functions

Kolk E.

Demonstratio Mathematica

2004

Vol. 37, nr 1

159--175

On some approximation problems in Musielak-Orlicz spaces of multifunctions

Kasperski A.

Demonstratio Mathematica

2004

Vol. 37, nr 2

393--406

We introduce the Musielak-Orlicz spaces of multifunctions Xmphi and Xc,m,phi. We prove that these spaces are complete. Also, we get some convergence and approximation theorems in these spaces.