scholarly journals Strong Convergence Theorems for Asymptotically WeakG-Pseudo-Ψ-Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yuanheng Wang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Generalized Projection ◽  
Iterative Sequence ◽  
Successive Approximation Method ◽  
Convergence Theorems ◽  
Mann Iterative Sequence ◽  
Sequence Method ◽  
Generalized Projection Method

A new concept of the asymptotically weakG-pseudo-Ψ-contractive non-self-mappingT:G↦Bis introduced and some strong convergence theorems for the mapping are proved by using the generalized projection method combined with the modified successive approximation method or with the modified Mann iterative sequence method in a uniformly and smooth Banach space. The proof methods are also different from some past common methods.

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

scholarly journals Approximation of viscosity zero points of accretive operators in a Banach space

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2175-2184
Author(s):  
Sun Cho ◽  
Shin Kang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Computational Errors ◽  
Zero Points

In this paper, zero points of m-accretive operators are investigated based on a viscosity iterative algorithm with double computational errors. Strong convergence theorems for zero points of m-accretive operators are established in a Banach space.

scholarly journals A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuanheng Wang ◽  
Huimin Shi
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Iterative Sequence ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Ishikawa Iterative Sequence

A new modified mixed Ishikawa iterative sequence with error for common fixed points of two asymptotically quasi pseudocontractive type non-self-mappings is introduced. By the flexible use of the iterative scheme and a new lemma, some strong convergence theorems are proved under suitable conditions. The results in this paper improve and generalize some existing results.

scholarly journals Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

2013 ◽  
Vol 21 (1) ◽  
pp. 183-200
Author(s):  
Prasit Cholamjiak ◽  
Yeol Je Cho ◽  
Suthep Suantai
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Duality Mapping ◽  
Convergence Theorems ◽  
Strictly Convex Banach Space ◽  
Differentiable Norm ◽  
Gauge Functions

Abstract In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.

scholarly journals Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
P. Cholamjiak ◽  
W. Cholamjiak ◽  
S. Suantai
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Equilibrium Problems ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Theorems ◽  
Viscosity Approximation Methods

AbstractIn this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

The Strong Convergence of a New Iterative Algorithm for Asymptotically Nonexpansive Mappings

2013 ◽  
Vol 756-759 ◽  
pp. 3628-3633
Author(s):  
Yuan Heng Wang ◽  
Wei Wei Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm

In a real Banach space E with a uniformly differentiable norm, we prove that a new iterative sequence converges strongly to a fixed point of an asymptotically nonexpansive mapping. The results in this paper improve and extend some recent results of other authors.

scholarly journals Convergence Theorems for Finite Family of Multivalued Maps in Uniformly Convex Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Yekini Shehu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Iterative Process ◽  
Real Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Multivalued Maps ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces

We introduce a new iterative process to approximate a common fixed point of a finite family of multivalued maps in a uniformly convex real Banach space and establish strong convergence theorems for the proposed process. Furthermore, strong convergence theorems for finite family of quasi-nonexpansive multivalued maps are obtained. Our results extend important recent results.

Sign in / Sign up

Export Citation Format

Share Document