scholarly journals New iteration process for a general class of contractive mappings

2016 ◽  
Vol 20 (2) ◽  
pp. 117
Author(s):  
Adesanmi Alao Mogbademu
Keyword(s):  
General Class ◽  
Iteration Process ◽  
Contractive Mappings

A Note on "Implicit Mann Fixed Point Iterations for Pseudo-Contractive Mappings"

2011 ◽  
Vol 393-395 ◽  
pp. 543-545
Author(s):  
Hong Jun Li ◽  
Yong Fu Su
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonempty Subset ◽  
Applied Mathematics ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Contractive Mappings ◽  
Contractive Map ◽  
Fixed Point Iterations ◽  
Implicit Iteration

Ljubomir Ciric, Arif Rafiq, Nenad Cakic, Jeong Sheok Umed [ Implicit Mann fixed point iterations for pseudo-contractive mappings, Applied Mathematics Letters 22 (2009) 581-584] introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the relatively convergence theorem. However, the content of mann theorem is fuzzy. In this paper, we will give some comments . Let be a Banach space and be a nonempty subset of . A mapping is called hemi-contractive (see [1]) if and In [1], the authors introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the following convergence theorem.

scholarly journals Convergence theorems for finite family of a general class of multi-valued strictly pseudo-contractive mappings

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Charles E Chidume ◽  
Mmaduabuchi E Okpala ◽  
Abdulmalik U Bello ◽  
Patrice Ndambomve
Keyword(s):  
General Class ◽  
Finite Family ◽  
Convergence Theorems ◽  
Contractive Mappings

scholarly journals An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography

2021 ◽  
Vol 6 (7) ◽  
pp. 6699-6714
Author(s):  
Ti-Ming Yu ◽  
◽  
Abdul Aziz Shahid ◽  
Khurram Shabbir ◽  
Yong-Min Li ◽  
...  
Keyword(s):  
General Class ◽  
Iteration Process ◽  
Convergence Stability

scholarly journals Some Generalizations of Non-Unique Fixed Point Theorems of Ćirić-type for (Φ, ψ)-Hybrid Contractive Mappings

2019 ◽  
Vol 33 (1) ◽  
pp. 221-234
Author(s):  
Memudu O. Olatinwo
Keyword(s):  
Fixed Point ◽  
General Class ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Contractive Mappings ◽  
Novi Sad ◽  
Similar Notion

AbstractIn this article, we establish some non-unique fixed point theorems of Ćirić’s type for (Φ, ψ)–hybrid contractive mappings by using a similar notion to that of the paper [M. Akram, A.A. Zafar and A.A. Siddiqui, A general class of contractions: A–contractions, Novi Sad J. Math. 38 (2008), no. 1, 25–33]. Our results generalize, extend and improve several ones in the literature.

scholarly journals S-iteration process for quasi-contractive mappings

2013 ◽  
Vol 2013 (1) ◽  
pp. 206 ◽  
Author(s):  
Vivek Kumar ◽  
Abdul Latif ◽  
Arif Rafiq ◽  
Nawab Hussain
Keyword(s):  
Iteration Process ◽  
Contractive Mappings

scholarly journals ON FIXED POINTS OF GENERALIZED SET-VALUED CONTRACTIONS

2009 ◽  
Vol 81 (1) ◽  
pp. 16-22 ◽  
Author(s):  
S. BENAHMED ◽  
D. AZÉ
Keyword(s):  
Fixed Point ◽  
Variational Method ◽  
Fixed Points ◽  
General Result ◽  
General Class ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Sharp Estimate ◽  
Complete Metric Spaces ◽  
Contractive Mappings

AbstractUsing a variational method introduced in [D. Azé and J.-N. Corvellec, ‘A variational method in fixed point results with inwardness conditions’, Proc. Amer. Math. Soc.134(12) (2006), 3577–3583], deriving directly from the Ekeland principle, we give a general result on the existence of a fixed point for a very general class of multifunctions, generalizing the recent results of [Y. Feng and S. Liu, ‘Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings’, J. Math. Anal. Appl.317(1) (2006), 103–112; D. Klim and D. Wardowski, ‘Fixed point theorems for set-valued contractions in complete metric spaces’, J. Math. Anal. Appl.334(1) (2007), 132–139]. Moreover, we give a sharp estimate for the distance to the fixed-points set.

scholarly journals Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings

2021 ◽  
Vol 34 (4) ◽  
pp. 78-92
Author(s):  
Zena Hussein Maibed ◽  
Ali Qasem Thajil
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Analytic Proof ◽  
Numerical Example ◽  
Contractive Mappings ◽  
Dependence Result

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

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