Convergence theorems for nonspreading mappings and nonexpansive multivalued mappings and equilibrium problems

2012 ◽  
Vol 7 (3) ◽  
pp. 547-557 ◽  
Author(s):  
Mohammad Eslamian
Keyword(s):  
Equilibrium Problems ◽  
Multivalued Mappings ◽  
Convergence Theorems ◽  
Nonspreading Mappings

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 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.

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