Approximation of elements of the spaces X^1_ϕ and X_ϕ by nonlinear, singular kernels

Andrzej Kasperski

Published: 1992-09-30
Language: EN

Vol. 6 (1992)

Approximation of elements of the spaces X^1_ϕ and X_ϕ by nonlinear, singular kernels

Andrzej Kasperski

Abstract

Let l^ϕ be a Musielak-Orlicz sequence space. Let X¹_ϕ and X_ϕ be the modular spaces of multifunctions generated by l^ϕ. Let K_w,j: R→R for j = 0,1,2,..., w∈W, where W is an abstract set of indices. Assuming certain singularity assumption on the nonlinear kernel K_w,j and setting T_w(F)=(T_w(F)(i))_i=0^∞ with (T_w(F))(i) = {Σ_j=0ⁱK_w,j(f(j)) : f(j)∈F(j)}, convergence theorems T_w(F)→_ϕ,????F in X¹_ϕ and T_w(F)→_d,ϕ,????F in X_ϕ are obtained.

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Kasperski, A. (1992). Approximation of elements of the spaces X^1_ϕ and X_ϕ by nonlinear, singular kernels. Annales Mathematicae Silesianae, 6, 21–29. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/14264

Vol. 6 (1992)
Published: 1992-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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