The article strong convergence theorems for approximation of common fixed points for a finite family of pseudocontractive mappings. It states that the approximation of an implicit iteration algorithm are proven in Banach spaces. Mathematicians introduce an implicit iteration process for a family of nonexpensive mappings which is illustrated in mathematical notation. On the other hand, other mathematicians proved the weak convergence of iterative process to a common fixed point of a finite family nonexpansive mappings in a Hilbert space.
Presents a research on the approximation of piecewise polynomial functions in the space c[0,1] by E. D. Livshits. Endowment of research by the Russian Foundation for Basic Research; Notation from Chebyshev on the subject; Theorems on continuous multiplicative selection; Construction of proofs of the theorems which involve metric projection, mathematical equations and functions and banach spaces.