In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed. [ABSTRACT FROM AUTHOR]
Al-Mezel, Saleh Abdullah, Ansari, Qamrul Hasan, and Ceng, Lu-Chuan
Subjects
FIXED point theory, VISCOSITY, ITERATIVE methods (Mathematics), ALGORITHMS, PROBLEM solving
Abstract
In this paper, we propose hybrid implicit and explicit viscosity iterative algorithms for solving general hierarchical fixed-point problems for a countable family of non-expansive mappings in uniformly smooth Banach spaces. These hybrid viscosity algorithms are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under suitable conditions. Our results extend, improve, supplement and develop the recent results in the literature. [ABSTRACT FROM PUBLISHER]
ITERATIVE methods (Mathematics), ALGORITHMS, GENERALIZATION, MATHEMATICAL inequalities, FIXED point theory, PROBLEM solving
Abstract
We propose an iterative scheme for finding a common element of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem in Euclidean space. Under some mild conditions, we establish the convergence theorem for the proposed algorithm. We also give a suitable condition to ensure the intersection of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem to be nonempty. In addition, under certain error bound conditions, we prove the convergence rate of the iterative sequence. Preliminary computational experience is also reported. [ABSTRACT FROM AUTHOR]