A new self-adaptive accelerated method for generalized split system of common fixed-point problem of averaged mappings

The purpose of this paper is to propose a new inertial self-adaptive algorithm for generalized split system of common fixed point problems of finite family of averaged mappings in the framework of Hilbert spaces. The weak convergence theorem of the proposed method is given and its theoretical application for solving several generalized problems is presented. The behavior and efficiency of the proposed algorithm is illustrated by some numerical tests.

Around averaged mappings

This paper is intended for a general mathematical audience. The examples show how the study of existence of fixed points of averaged mappings $$T_{\lambda }= (1-\lambda )I+ \lambda T$$ T λ = ( 1 - λ ) I + λ T , where $$0<\lambda <1$$ 0 < λ < 1 and I is the identity operator, can help in the study of existence of fixed points of mappings T.

A Hybrid Gradient-Projection Algorithm for Averaged Mappings in Hilbert Spaces

It is well known that the gradient-projection algorithm (GPA) is very useful in solving constrained convex minimization problems. In this paper, we combine a general iterative method with the gradient-projection algorithm to propose a hybrid gradient-projection algorithm and prove that the sequence generated by the hybrid gradient-projection algorithm converges in norm to a minimizer of constrained convex minimization problems which solves a variational inequality.