Approximation of elements of the spaces X^1_ϕ and X_ϕ by nonlinear, singular kernels
Abstract
Let lϕ be a Musielak-Orlicz sequence space. Let X1ϕ and Xϕ be the modular spaces of multifunctions generated by lϕ. Let Kw,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 Kw,j and setting Tw(F)=(Tw(F)(i))i=0∞ with (Tw(F))(i) = {Σj=0iKw,j(f(j)) : f(j)∈F(j)}, convergence theorems Tw(F)→ϕ,𝓦 F in X1ϕ and Tw(F)→d,ϕ,𝓦 F in Xϕ are obtained.
References
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Instytut Matematyki, Politechnika Śląska Poland
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