scholarly journals On Strong Convergence of Halpern’s Method Using Averaged Type Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
F. Cianciaruso ◽  
G. Marino ◽  
A. Rugiano ◽  
B. Scardamaglia
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Common Fixed Points ◽  
Nonspreading Mapping ◽  
Control Coefficients

Under suitable hypotheses on control coefficients, we study Halpern’s method to approximate strongly common fixed points of a nonexpansive mapping and of a nonspreading mapping or a fixed point of one of them. A crucial tool in our results is the regularization with the averaged type mappings.

scholarly journals On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nawab Hussain ◽  
Giuseppe Marino ◽  
Afrah A. N. Abdou
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Nonspreading Mapping ◽  
Type Mapping ◽  
Nonspreading Mappings

In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Strong andΔ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0)Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
C. E. Chidume ◽  
A. U. Bello ◽  
P. Ndambomve
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Common Fixed Points ◽  
Finite Family ◽  
Iterative Sequence ◽  
Convergence Theorems ◽  
The Family ◽  
Demicontractive Mappings ◽  
Nonlinear Mappings

LetKbe a nonempty closed and convex subset of a complete CAT(0) space. LetTi:K→CBK,i=1,2,…,m, be a family of multivalued demicontractive mappings such thatF:=⋂i=1mF(Ti)≠∅. A Krasnoselskii-type iterative sequence is shown toΔ-converge to a common fixed point of the familyTi,i=1,2,…,m. Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT(0)spaces. Furthermore, our method of the proof is of special interest.

scholarly journals ON STRONG CONVERGENCE OF HALPERN’S METHOD FOR QUASI-NONEXPANSIVE MAPPINGS IN HILBERT SPACES

2016 ◽  
Vol 21 (1) ◽  
pp. 63-82 ◽  
Author(s):  
Jesus Garcia Falset ◽  
Enrique Llorens-Fuster ◽  
Giuseppe Marino ◽  
Angela Rugiano
Keyword(s):  
Hilbert Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Type Method ◽  
Numerical Example

In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.

scholarly journals Common fixed points of single-valued and multivalued maps

2005 ◽  
Vol 2005 (19) ◽  
pp. 3045-3055 ◽  
Author(s):  
Yicheng Liu ◽  
Jun Wu ◽  
Zhixiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Partial Answer ◽  
Multivalued Maps ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems

We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.

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 An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

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