Open AccessSimplification method for nonlinear equations of monotone type in Banach space
Author(s) -
I. P. Ryazantseva
Publication year - 2021
Publication title -
žurnal srednevolžskogo matematičeskogo obŝestva
Language(s) - English
Resource type - Journals
eISSN - 2587-7496
pISSN - 2079-6900
DOI - 10.15507/2079-6900.23.202102.185-192
Subject(s) - pseudo monotone operator , mathematics , finite rank operator , compact operator , banach space , mathematical analysis , semi elliptic operator , strictly singular operator , operator space , c0 semigroup , monotone polygon , operator (biology) , approximation property , regularization (linguistics) , pure mathematics , differential operator , computer science , biochemistry , chemistry , geometry , repressor , artificial intelligence , transcription factor , extension (predicate logic) , gene , programming language
. In a Banach space, we study an operator equation with a monotone operator T. The operator is an operator from a Banach space to its conjugate, and T=AC, where A and C are operators of some classes. The considered problem belongs to the class of ill-posed problems. For this reason, an operator regularization method is proposed to solve it. This method is constructed using not the operator T of the original equation, but a more simple operator A, which is B-monotone, B=C−1. The existence of the operator B is assumed. In addition, when constructing the operator regularization method, we use a dual mapping with some gauge function. In this case, the operators of the equation and the right-hand side of the given equation are assumed to be perturbed. The requirements on the geometry of the Banach space and on the agreement conditions for the perturbation levels of the data and of the regularization parameter are established, which provide a strong convergence of the constructed approximations to some solution of the original equation. An example of a problem in Lebesgue space is given for which the proposed method is applicable.