We consider the problems of correct finding of normal quasisolutions of operator equations whose operator is a superposition of linear and nonlinear operators. The nonlinear operator is a modulo operation. In the case where the linear operator is completely continuous, we establish sufficient conditions for the regularization parameter guaranteeing the convergence of the solution of regularized problem to the quasisolution of the exact operator equation depending on the error of the linear operator of the problem.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 4, pp. 63–72, October–December, 2020.
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Topolyuk, Y.P. Convergence of the Method of Regularization for Finding Normal Quasisolutions in Problems with Free Phase and a Completely Continuous Operator. J Math Sci 273, 960–971 (2023). https://doi.org/10.1007/s10958-023-06557-0
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DOI: https://doi.org/10.1007/s10958-023-06557-0