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Title:
Study of high-order iterative methods for approximation of polynomial zeros and fixed points of quasi-contraction maps in metric spaces.
The aim of the project:
The proposed project is dedicated to the study of the convergence of high-order iterative methods for approximation of polynomial zeros and to the problem of obtaining existence and approximation fixed point theorems for quasi-contraction mappings in metric spaces. These two problems form two large areas of modern mathematics that are closely interrelated. They are among the most contemporary mathematical problems and have numerous applications in both theoretical and applied research. Midst most basic applications of the iterative methods are the numerical solving polynomial equations with coefficients in arbitrary normed field and the numerical solving operator equations in Banach spaces.