scholarly journals Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 72
Author(s):  
Jong Soo Jung
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Reflexive Banach Space ◽  
Convex Combination ◽  
Duality Mapping ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings ◽  
Weakly Continuous ◽  
Weakly Continuous Duality Mapping

In this paper, first, we introduce a path for a convex combination of a pseudocontractive type of mappings with a perturbed mapping and prove strong convergence of the proposed path in a real reflexive Banach space having a weakly continuous duality mapping. Second, we propose two modified implicit iterative methods with a perturbed mapping for a continuous pseudocontractive mapping in the same Banach space. Strong convergence theorems for the proposed iterative methods are established. The results in this paper substantially develop and complement the previous well-known results in this area.

scholarly journals Convergence of iterative algorithms for continuous pseudocontractive mappings

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1767-1777 ◽  
Author(s):  
Jong Jung
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Convex Combination ◽  
Iterative Algorithms ◽  
Duality Mapping ◽  
Pseudocontractive Mapping ◽  
Pseudocontractive Mappings ◽  
Weakly Continuous ◽  
Weakly Continuous Duality Mapping ◽  
Implicit Iterative Algorithm

In this paper, we prove strong convergence of a path for a convex combination of a pseudocontractive type of operators in a real reflexive Banach space having a weakly continuous duality mapping J? with gauge function ?. Using path convergency, we establish strong convergence of an implicit iterative algorithm for a pseudocontractive mapping combined with a strongly pseudocontractive mapping in the same Banach space.

scholarly journals The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Pakkapon Preechasilp
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Methods ◽  
Reflexive Banach Space ◽  
Iterative Scheme ◽  
Duality Mapping ◽  
Nonexpansive Semigroups ◽  
Weakly Continuous ◽  
Asymptotically Nonexpansive ◽  
Weakly Continuous Duality Mapping

We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

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 The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Rabian Wangkeeree
Keyword(s):  
Reflexive Banach Space ◽  
Nonexpansive Mappings ◽  
Linear Operators ◽  
Duality Mapping ◽  
Approximation Methods ◽  
Iterative Approximation ◽  
Bounded Linear ◽  
Weakly Continuous ◽  
Weakly Continuous Duality Mapping ◽  
Hybrid Approximation

We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009).

scholarly journals General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Peichao Duan ◽  
Aihong Wang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding results reported by many others.

Iterative Methods for Strictly Pseudo-Contractive Mappings

2013 ◽  
Vol 333-335 ◽  
pp. 1402-1405
Author(s):  
Yang Liu ◽  
Yan Hao
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Smooth Banach Space ◽  
Convergence Theorems ◽  
Uniformly Smooth Banach Space ◽  
Contractive Mappings ◽  
Uniformly Smooth

The aim of this work is to consider an iterative method for a-strict pseudo-contractions. Strong convergence theorems are established in a real 2-uniformly smooth Banach space.

scholarly journals A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Kamonrat Nammanee ◽  
Suthep Suantai ◽  
Prasit Cholamjiak
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Reflexive Banach Space ◽  
Duality Mapping ◽  
Nonexpansive Semigroup ◽  
Gauge Functions ◽  
Implicit And Explicit ◽  
General Iterative Method

We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mappingJφ, whereφis a gauge function on[0,∞). Our results improve and extend those announced by G. Marino and H.-K. Xu (2006) and many authors.

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.

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 Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptoticallyk-Strict Pseudocontractive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Important Class ◽  
Convergence Theorems ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptoticallyk-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

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