منابع مشابه
Some Stability Results for Picard Iterative Process in Uniform Space
The following concepts shall be required in the sequel: Definition 1.1 [5, 27]. A uniform space (X,Φ) is a nonempty set X equipped with a nonempty family Φ of subsets of X ×X satisfying the following properties: (i) if U is in Φ, then U contains the diagonal {(x, x) |x ∈ X}; (ii) if U is in Φ and V is a subset of X ×X which contains U, then V is in Φ; (iii) if U and V are in Φ, then U ∩ V is in...
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In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators. We also give convergence and stability analysis of the new Picard-Mann iterative approximation and propose numerical examples to show that the new Picard-Mann iteration converges more effectively than the Picard ite...
متن کاملWeak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings
The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...
متن کاملStrong Convergence Theorems of Modified Mann Iterative Process for Nonexpansive Mappings in Hilbert Spaces
The purpose of this article is to modify normal Mann’s iterative process to have strong convergence for nonexpansive mappings in the formework of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the fixed point of nonexpansive mappings which is the unique solution of a variational inequality, which is also the optimality condition for a minimization problem.
متن کاملA Comparison of Picard and Mann Iterations for Quasi-contraction Maps
For a class of quasi-contractive operators defined on an arbitrary Banach space, it has been shown that the Picard iteration technique converges faster than the Mann iteration technique. In this paper we make a comparison of the Picard and Mann iterations with respect to their convergence rate for a more general class of operators called quasi-contractions in metrizable topological vector space...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2013
ISSN: 1687-1812
DOI: 10.1186/1687-1812-2013-69