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期刊论文
APPROXIMATE SOLUTIONS OF OPERATOR EQUATIONS
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The study of operator equations is an important branch of mathematics. The fundamental theory of operator equations, linear or nonlinear, formulated in a Hilbert or a Banach space setting, is originated from the classical theory of differential and integral equations. This modern theory of differential and integral equations has been well developed in the last few decades, in which many profound concepts, results, methods, and algorithms were established with considerable generality. On the one hand, various types of mathematical equations, such as linear and nonlinear differential, integral, integro-differential, and functional equations, can all be unified under the same framework of abstract operator equations. On the other hand, many well-known theories and methods in Functional Analysis and Operator Theory have proven very effective and useful in the study of basic solvability problems in operator equations, including not only the existence and uniqueness of a solution but also efficient numerical algorithms for approximating the solution. The theory and methodology of operator equations have now played a very important role in computational mathematics, applied sciences and engineering.
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