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Title: Inhomogeneous poly-scale refinement type equations and Markov operators with perturbations
Authors: Kapica, Rafał
Morawiec, Janusz
Keywords: Inhomogeneous poly-scale refinement type equations; Markov operators with perturbations; fixed points; Lp-solutions; continuous and bounded solutions; compactly supported solutions
Issue Date: 2015
Citation: Journal of Fixed Point Theory and Applications, Vol. 17, iss. 3 (2015), s. 507-520
Abstract: Given measure spaces (Ω1,A1,μ1), . . . , (ΩN,AN,μN), functions φ1 : Rm×Ω1 Rm, . . . ,φN : Rm×ΩN Rm and g : Rm R, we present results on the existence of solutions f : Rm R of the inhomogeneous poly-scale refinement type equation of the form f(x) = ΣN n=1 ∫ Ωn det(φn)′x(x, ωn) f (φn(x, ωn)) dμn(ωn) + g(x) in some special classes of functions. The results are obtained by Banach fixed point theorem applied to a perturbed Markov operator connected with the considered inhomogeneous poly-scale refinement type equation. Mathematics Subject Classification. Primary 37H99, 37N99; Secondary 39B12.
DOI: 10.1007/s11784-015-0226-3
ISSN: 1661-7738
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