scholarly journals Strong and weak convergence of an iterative process for a finite family of multivalued mappings satisfying the condition (C)

2017 ◽  
Vol 66 (1) ◽  
pp. 51-65
Author(s):  
YILDIRIM İsa
Keyword(s):  
Weak Convergence ◽  
Iterative Process ◽  
Finite Family ◽  
Multivalued Mappings ◽  
Strong And Weak Convergence ◽  
Condition C

scholarly journals On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaolong Qin ◽  
Jong Kyu Kim ◽  
Tianze Wang
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Fixed Points ◽  
Iterative Process ◽  
Real Hilbert Space ◽  
Common Fixed Points ◽  
Finite Family ◽  
Strong And Weak Convergence ◽  
Pseudocontractive Mappings ◽  
Asymptotically Pseudocontractive Mappings

An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.

scholarly journals Strong and Weak Convergence Theorems for Equilibrium Problems and Weak Relatively Uniformly Nonexpansive Multivalued Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Zi-Ming Wang
Keyword(s):  
Weak Convergence ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Common Element ◽  
Multivalued Mappings ◽  
Point Problem ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
The Common

Equilibrium problem and fixed point problem are considered. A general iterative algorithm is introduced for finding a common element of the set of solutions to the equilibrium problem and the common set of fixed points of two weak relatively uniformly nonexpansive multivalued mappings. Furthermore, strong and weak convergence results for the common element in the two sets mentioned above are established in some Banach space.

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 On the JK Iterative Process in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Junaid Ahmad ◽  
Hüseyin Işık ◽  
Faeem Ali ◽  
Kifayat Ullah ◽  
Eskandar Ameer ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
The Other ◽  
Iterative Schemes ◽  
Strong And Weak Convergence ◽  
Nonexpansive Maps ◽  
Iterative Procedures

In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α -nonexpansive mappings. Secondly, by constructing an example of generalized α -nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature.

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 A New Approximation Method for Common Fixed Points of a Finite Family of Generalized Asymptotically Quasinonexpansive Mappings in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Pornsak Yatakoat ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Approximation Method ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Finite Family ◽  
Strong And Weak Convergence

We introduce a new iterative scheme to approximate a common fixed point for a finite family of generalized asymptotically quasinonexpansive mappings. Several strong and weak convergence theorems of the proposed iteration in Banach spaces are established. The main results obtianed in this paper generalize and refine many known results in the current literature.

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