scholarly journals Convergence results for modified SP-iteration in uniformly convex metric spaces

2021 ◽  
Vol 26 (02) ◽  
pp. 162-171
Author(s):  
P. Sukprasert ◽  
V. Yang ◽  
R. Khunprasert ◽  
W. Khuangsatung
Keyword(s):  
Metric Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Convex Metric Spaces

scholarly journals On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces

2021 ◽  
Vol 37 (3) ◽  
pp. 513-527
Author(s):  
JENJIRA PUIWONG ◽  
◽  
SATIT SAEJUNG ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Fixed Point Set ◽  
Convergence Theorems ◽  
Convex Metric Spaces ◽  
Strict Fixed Point ◽  
Point Set

We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.

scholarly journals Fixed Points for Multivalued Mappings in Uniformly Convex Metric Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
A. Kaewcharoen ◽  
B. Panyanak
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Uniformly Convex ◽  
Convex Metric Spaces ◽  
Weakly Inward

The purpose of this paper is to ensure the existence of fixed points for multivalued nonexpansive weakly inward nonself-mappings in uniformly convex metric spaces. This extends a result of Lim (1980) in Banach spaces. All results of Dhompongsa et al. (2005) and Chaoha and Phon-on (2006) are also extended.

scholarly journals Fixed point iterations for Prešić-Kannan nonexpansive mappings in product convex metric spaces

2018 ◽  
Vol 10 (1) ◽  
pp. 56-69
Author(s):  
Hafiz Fukhar-ud-din ◽  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Product Spaces ◽  
Convex Metric Spaces ◽  
Fixed Point Iterations

Abstract We introduce Prešić-Kannan nonexpansive mappings on the product spaces and show that they have a unique fixed point in uniformly convex metric spaces. Moreover, we approximate this fixed point by Mann iterations. Our results are new in the literature and are valid in Hilbert spaces, CAT(0) spaces and Banach spaces simultaneously.

Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3573-3583
Author(s):  
Hafiz Fukhar-ud-dina ◽  
Safeer Khan
Keyword(s):  
Iterative Algorithm ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
Special Cases ◽  
Total Asymptotically Nonexpansive Mappings

We introduce and study a three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in a uniformly convex metric space. The proposed algorithm includes Mann and Ishikawa iterative algorithms, the iterative algorithm of Khan and Takahashi [13] and the three-step iterative algorithm of Xu and Noor [26] as special cases. Our results are new and generalize several recent results in Hilbert spaces, uniformly convex Banach spaces and CAT (0) spaces, simultaneously.

scholarly journals Δ-Convergence of Products of Operators in p-Uniformly Convex Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 741
Author(s):  
Byoung Jin Choi
Keyword(s):  
Weak Convergence ◽  
Metric Spaces ◽  
Projection Operators ◽  
Uniformly Convex ◽  
Nonexpansive Maps ◽  
Convex Metric Spaces

In this paper, we first introduce the new notion of p-strongly quasi-nonexpansive maps on p-uniformly convex metric spaces, and then we study the Δ (weak)-convergence of products of p-strongly quasi-nonexpansive maps on p-uniformly convex metric spaces. Furthermore, using the result, we prove the Δ -convergence of the weighted averaged method for projection operators.

scholarly journals Proximal-type algorithms for split minimization problem in P-uniformly convex metric spaces

2018 ◽  
Vol 82 (3) ◽  
pp. 909-935 ◽  
Author(s):  
C. Izuchukwu ◽  
G. C. Ugwunnadi ◽  
O. T. Mewomo ◽  
A. R. Khan ◽  
M. Abbas
Keyword(s):  
Minimization Problem ◽  
Metric Spaces ◽  
Uniformly Convex ◽  
Convex Metric Spaces

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.

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