A Sufficiency and Necessity Condition on Convergence of Ishikawa Iterative Process for Asymptotically Pseudocontractive Mapping

2010 ◽  
Author(s):  
Hongshan Du ◽  
Guanglan Wang
Keyword(s):  
Iterative Process ◽  
Pseudocontractive Mapping ◽  
Ishikawa Iterative Process ◽  
Asymptotically Pseudocontractive Mapping

scholarly journals Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings

2019 ◽  
Vol 12 (2) ◽  
pp. 348-357
Author(s):  
Safeer Hussain Khan ◽  
Hira Iqbal ◽  
Mujahid Abbas
Keyword(s):  
Fixed Points ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Ishikawa Iterative Process

In this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic spaces.

scholarly journals Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Wiyada Kumam ◽  
Usa Humphries ◽  
Poom Kumam
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Infinite Family ◽  
Strong Convergence Theorem ◽  
Mild Conditions ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Ishikawa Iterative Process

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudocontractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature.

Sign in / Sign up

Export Citation Format

Share Document