scholarly journals One-step iterative process for a finite family of multivalued mappings

2011 ◽  
Vol 54 (1-2) ◽  
pp. 105-111 ◽  
Author(s):  
Mohammad Eslamian ◽  
Ali Abkar
Keyword(s):  
Iterative Process ◽  
Finite Family ◽  
Multivalued Mappings ◽  
One Step

scholarly journals Convergence theorems for nonspreading mappings and equilibrium problems in Hadamard spaces

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1863-1874
Author(s):  
Davood Afkhamitaba ◽  
Hossein Dehghan
Keyword(s):  
Iterative Process ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Finite Family ◽  
Common Element ◽  
Multivalued Mappings ◽  
Hadamard Space ◽  
Convergence Theorems ◽  
Nonspreading Mappings

In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of nonspreading mappings and a finite family of nonexpansive multivalued mappings in Hadamard space. We state and prove strong and ? convergence theorems of the proposed iterative process. The results obtained in this paper extend and improve some recent known results.

scholarly journals An iterative process for a hybrid pair of generalized I-asymptotically nonexpansive single-valued mappings and generalized nonexpansive multi-valued mappings in Banach spaces

2018 ◽  
Vol 34 (1) ◽  
pp. 31-45
Author(s):  
ALI FARAJZADEH ◽  
◽  
PREEYANUCH CHUASUK ◽  
ANCHALEE KAEWCHAROEN ◽  
MOHAMMAD MURSALEEN ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Hybrid Pair

In this paper, an iterative process for a hybrid pair of a finite family of generalized I-asymptotically nonexpansive single-valued mappings and a finite family of generalized nonexpansive multi-valued mappings is established. Moreover, the weak convergence theorems and strong convergence theorems of the proposed iterative process in Banach spaces are proven. The examples are established for supporting our main results. The obtained results can be viewed as an improvement and extension of the several results in the literature.

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.

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.

scholarly journals Convergence Theorems for a Common Point of Solutions of Equilibrium and Fixed Point of Relatively Nonexpansive Multivalued Mapping Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Banach Spaces ◽  
Multivalued Mapping ◽  
Iterative Process ◽  
Common Point ◽  
Finite Family ◽  
Relatively Nonexpansive ◽  
Nonexpansive Multivalued Mapping

We introduce an iterative process which converges strongly to a common point of set of solutions of equilibrium problem and set of fixed points of finite family of relatively nonexpansive multi-valued mappings in Banach spaces.

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