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- W1978502340 abstract "Given measure spaces $${(Omega_{1}, mathcal{A}_{1}, mu_{1}),...,(Omega_{N}, mathcal{A}_{N}, mu_{N}),}$$ functions $${varphi_{1}: mathbb{R}^{m} times Omega_{1} rightarrow mathbb{R}^{m},...,varphi_{N}: mathbb{R}^{m} times Omega_{N} rightarrow mathbb{R}^{m}}$$ and $${g: mathbb{R}^{m} rightarrow mathbb{R}}$$ , we present results on the existence of solutions $${f: mathbb{R}^{m} rightarrow mathbb{R}}$$ of the inhomogeneous poly-scale refinement type equation of the form $$f(x) = sum_{n=1}^{N} int_{Omega_{n}}|{rm det}(varphi_{n})^{prime} _{x}(x, omega_{n})|f(varphi_{n}(x, omega_{n}))dmu_{n}(omega_{n}+g(x)$$ 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." @default.
- W1978502340 created "2016-06-24" @default.
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- W1978502340 date "2015-04-05" @default.
- W1978502340 modified "2023-10-14" @default.
- W1978502340 title "Inhomogeneous poly-scale refinement type equations and Markov operators with perturbations" @default.
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- W1978502340 doi "https://doi.org/10.1007/s11784-015-0226-3" @default.
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