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The aim of this work is to develop an S-iteration technique for finding common fixed points for nonself quasi-nonexpansive mappings in the framework of a uniformly convex Banach space. Convergence properties of the proposed algorithm are analyzed in the setting of uniformly convex Banach spaces. To prove the usability of our results, some novel applications are provided, focused on zeros of accretive operators, convex programming, and feasibility problems. Some numerical experiments with real datasets for Lasso problems are provided. [ABSTRACT FROM AUTHOR]

The Mann iterates behave well for nonexpansive mappings for any initial guess in the domain. Our aim in this article is to extend this method to a broad class of inexact fixed point algorithms generated by nearly nonexpansive sequences in Banach spaces and to locate the weak limit of the iterates by its initial guesses. Due to the inexactness, our algorithms become efficiently applicable for a wider class of problems. As applications, we give convergence theorems for finding solutions of variational inclusion problems and constrained multiple-sets split feasibility problems. Our results are significant refinements and improvements of the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the semilocal convergence analysis of a Newton-like method discussed by Bartle (Amer Math Soc 6: 827-831, ) to solve the generalized operator equations containing nondifferentiatble term in Banach spaces. This method has also been studied by Rheinboldt (SIAM J Numer Anal 5: 42-63, ). The aim of the paper is to discuss the convergence analysis under local Lipschitz condition $\|F'_{x}-F'_{x_{0}}\|\le \omega (\|x-x_{0}\|)$ for a given point $x_{0}$. Our results extend and improve the previous ones in the sense of local Lipschitz conditions. We apply our results to solve the Fredholm-type operator equations. [ABSTRACT FROM AUTHOR]

In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature. [ABSTRACT FROM AUTHOR]