APPLICATIONS OF STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE AND INVERSE-STRONGLY MONOTONE SEQUENCE OF MAPPINGS

2018 ◽  
Vol 10 (3) ◽  
pp. 121-141
Author(s):  
M. H. Ahmed Yahya ◽  
Adam Zakria ◽  
Ibrahim Elkhalil ◽  
Husam Alfadil
Keyword(s):  
Strong Convergence ◽  
Monotone Sequence ◽  
Convergence Theorems ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone

scholarly journals Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Bin-Chao Deng ◽  
Tong Chen
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Real Hilbert Space ◽  
Convergence Theorems ◽  
Mild Conditions ◽  
Strongly Monotone

LetHbe a real Hilbert space. LetT1,T2:H→Hbek1-,k2-strictly pseudononspreading mappings; letαnandβnbe two real sequences in (0,1). For givenx0∈H, the sequencexnis generated iteratively byxn+1=βnxn+1-βnTw1αnγfxn+I-μαnBTw2xn,∀n∈N, whereTwi=1−wiI+wiTiwithi=1,2andB:H→His strongly monotone and Lipschitzian. Under some mild conditions on parametersαnandβn, we prove that the sequencexnconverges strongly to the setFixT1∩FixT2of fixed points of a pair of strictly pseudononspreading mappingsT1andT2.

scholarly journals Δ-convergence theorems for inverse-strongly monotone mappings in CAT(0) spaces

2018 ◽  
Vol 19 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Sattar Alizadeh ◽  
◽  
Hossein Dehghan ◽  
Fridoun Moradlou ◽  
◽  
...  
Keyword(s):  
Monotone Mappings ◽  
Convergence Theorems ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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