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On pointwise convergence of nets of Mellin-Kantorovich convolution operators

Bardaro C., Mantellini I.

Commentationes Mathematicae

2013

Vol. 53, No. 2

65--77

Here we study pointwise approximation and asymptotic formulae for a class of Mellin-Kantorovich type integral operators, both in linear and nonlinear form.

On bounded solutions of second order systems

Herzog G.

Demonstratio Mathematica

2006

Vol. 39, nr 4

793-801

We prove existence and uniqueness of bounded solutions of u"+f(t, u) = 0, u(0) = x on [0,infinity) under quasimonotonicity and one-sided Lipschitz conditions on f.

Urysohn integral operators with homogeneous kernel : approximation properties in modular spaces

Bardaro C., Vinti G.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

[Z] 42(2)

145-182

Here we state some modular approximation theorems for a class of nonlinear integral operators, acting on functions defined on locally compact groups, whose kernels satisfy some Lipschitz conditions and some general homogeneity assumptions. Moreover we study the order of modular approximation in modular Lipschitz classes. Applications to nonlinear Mellin convolution operators are given.