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
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.
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Kapica, R., Morawiec, J. Inhomogeneous poly-scale refinement type equations and Markov operators with perturbations. J. Fixed Point Theory Appl. 17, 507–520 (2015). https://doi.org/10.1007/s11784-015-0226-3
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DOI: https://doi.org/10.1007/s11784-015-0226-3