scholarly journals Strong convergence theorems for multivalued $alpha$-demicontractive and $alpha$-hemicontractive mappings

2019 ◽  
Vol 7 (1) ◽  
pp. 1-6
Author(s):  
Apurva Kumar Das ◽  
Shailesh Dhar Diwan
Keyword(s):  
Strong Convergence ◽  
Convergence Theorems ◽  
Hemicontractive Mappings

Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

2020 ◽  
Vol 26 (2) ◽  
pp. 221-229
Author(s):  
Godwin C. Ugwunnadi ◽  
Chinedu Izuchukwu ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Metric Spaces ◽  
Iteration Process ◽  
Uniformly Convex ◽  
Convex Metric Space ◽  
Convergence Theorems ◽  
Uniformly Convex Metric Space ◽  
Convex Metric Spaces ◽  
Hemicontractive Mappings

AbstractIn this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

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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