scholarly journals Convergence of an Ishikawa iteration scheme for nonlinear quasi-contractive mappings in convex metric spaces

2001 ◽  
Vol 32 (2) ◽  
pp. 117-126
Author(s):  
K. P. R. Sastry ◽  
G. V. R. Babu ◽  
Ch. Srinivasa Rao
Keyword(s):  
Fixed Point ◽  
Convex Subset ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Iteration Scheme ◽  
Nonempty Closed Convex Subset ◽  
Convex Metric Space ◽  
Ishikawa Iteration ◽  
Contractive Mappings ◽  
Convex Metric Spaces

In this paper, we show that the Ishikawa iteration scheme for a nonlinear quasicontractive selfmap of a nonempty closed convex subset of a complete convex metric space, converges to the unique fixed point. Our theorem generalizes Ciric's result (1999) and partially solves an open problem of Ciric [5].

scholarly journals Common fixed point theorems for contractive mappings satisfying Φ-maps in S-metric spaces

2016 ◽  
Vol 8 (2) ◽  
pp. 298-311 ◽  
Author(s):  
Shaban Sedghi ◽  
Mohammad Mahdi Rezaee ◽  
Tatjana Došenović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Mappings ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

Abstract In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.

Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces

2008 ◽  
Vol 15 (1) ◽  
pp. 39-43
Author(s):  
Ljubomir B. Ćirić ◽  
Nebojša T. Nikolić
Keyword(s):  
Metric Space ◽  
Convex Subset ◽  
Metric Spaces ◽  
Satisfy Condition ◽  
Convex Metric Space ◽  
Convex Metric Spaces ◽  
The Family

Abstract Let (𝑋, 𝑑) be a convex metric space, 𝐶 be a closed and convex subset of 𝑋 and let 𝐵(𝐶) be the family of all nonempty bounded subsets of 𝐶. In this paper some results are obtained on the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings 𝑆,𝑇 : 𝐶 → 𝐵(𝐶) which satisfy condition (2.1) below.

scholarly journals Approximation of Fixed Points of C*-Algebra-Multi-Valued Contractive Mappings by the Mann and Ishikawa Processes in Convex C*-Algebra-Valued Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 392
Author(s):  
Azadeh Ghanifard ◽  
Hashem Parvaneh Masiha ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Infinite Family ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
C Algebra ◽  
Contractive Mappings

The aim of the present paper is to state and prove some convergence theorems for the Mann and Ishikawa iteration schemes involving C * -algebra-multi-valued contractive mappings in the setting of convex C * -algebra-valued metric spaces. The convergence theorems of the proposed iterations to a common fixed point of finite and infinite family of such mappings are also established.

scholarly journals Strong Convergence for Hybrid ImplicitS-Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shin Min Kang ◽  
Arif Rafiq ◽  
Faisal Ali ◽  
Young Chel Kwun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Banach Space ◽  
Iteration Scheme ◽  
Nonempty Closed Convex Subset ◽  
Pseudocontractive Mappings

LetKbe a nonempty closed convex subset of a real Banach spaceE, letS:K→Kbe nonexpansive, and let  T:K→Kbe Lipschitz strongly pseudocontractive mappings such thatp∈FS∩FT=x∈K:Sx=Tx=xandx-Sy≤Sx-Sy and x-Ty≤Tx-Tyfor allx, y∈K. Letβnbe a sequence in0, 1satisfying (i)∑n=1∞βn=∞; (ii)limn→∞⁡βn=0.For arbitraryx0∈K, letxnbe a sequence iteratively defined byxn=Syn, yn=1-βnxn-1+βnTxn, n≥1.Then the sequencexnconverges strongly to a common fixed pointpofSandT.

scholarly journals Note on Common Fixed Point Theorems in Convex Metric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 28
Author(s):  
Anil Kumar ◽  
Aysegul Tas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Convex Metric Space ◽  
Correct Version ◽  
Convex Metric Spaces ◽  
Set Up ◽  
Common Fixed Point Theorems

In the present paper, we pointed out that there is a gap in the proof of the main result of Rouzkard et al. (The Bulletin of the Belgian Mathematical Society 2012). Then after, utilizing the concept of (E.A.) property in convex metric space, we obtained an alternative and correct version of this result. Finally, it is clarified that in the theory of common fixed point, the notion of (E.A.) property in the set up of convex metric space develops some new dimensions in comparison to the hypothesis that a range set of one map is contained in the range set of another map.

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.

scholarly journals Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
Shiv Kant Tiwari ◽  
Vishnu Narayan Mishra ◽  
Idrees A. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Distance Functions ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Partial Metric Spaces

We establish some unique fixed point theorems in complete partial metric spaces for generalized weaklyS-contractive mappings, containing two altering distance functions under certain assumptions. Also, we discuss some examples in support of our main results.

scholarly journals Unique Fixed Point Theorem for Weakly C-Contractive Mappings

1970 ◽  
Vol 5 (1) ◽  
pp. 6-13 ◽  
Author(s):  
Binayak S Choudhury
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Engineering And Technology ◽  
Existing Result

In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces. Key words: Metric space; Fixed point; Weak C-contraction. M S C (2000): 54H25   DOI: 10.3126/kuset.v5i1.2842 Kathmandu University Journal of Science, Engineering and Technology Vol.5, No.1, January 2009, pp 6-13

scholarly journals Iterative approximation of fixed point forΦ-hemicontractive mapping without Lipschitz assumption

2005 ◽  
Vol 2005 (17) ◽  
pp. 2711-2718
Author(s):  
Xue Zhiqun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Real Banach Space ◽  
Unique Fixed Point ◽  
Nonempty Closed Convex Subset ◽  
Iterative Sequence ◽  
Iterative Approximation ◽  
Ishikawa Iterative Sequence ◽  
Uniformly Continuous

LetEbe an arbitrary real Banach space and letKbe a nonempty closed convex subset ofEsuch thatK+K⊂K. Assume thatT:K→Kis a uniformly continuous andΦ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point ofT.

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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