Published August 6, 2019 | Version v1
Publication Open

Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings

Creators

  • 1. King Mongkut's University of Technology Thonburi
  • 2. University of Electronic Science and Technology of China
  • 3. Gyeongsang National University
  • 4. Rajamangala University of Technology Phra Nakhon

Description

In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern's algorithm.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

في هذه الورقة، نقدم فئة جديدة من تعيينات بريغمان المعممة α - nonexpansive من حيث مسافة بريغمان. نؤسس العديد من نظريات التقارب الضعيفة والقوية لمخططات إيشيكاوا ونور التكرارية لمخططات بريغمان المعممة α - nonexpansive في مساحات بنك. يتم إعطاء مثال رقمي لتوضيح النتائج الرئيسية لتقريب النقطة الثابتة باستخدام خوارزمية هالبرن.

Translated Description (French)

Dans cet article, nous introduisons une nouvelle classe de mappages généralisés α -nonexpansifs de Bregman en termes de distance de Bregman. Nous établissons plusieurs théorèmes de convergence faibles et forts des schémas itératifs d'Ishikawa et de Noor pour les mappages α -nonexpansifs généralisés de Bregman dans les espaces de Banach. Un exemple numérique est donné pour illustrer les principaux résultats de l'approximation en point fixe à l'aide de l'algorithme de Halpern.

Translated Description (Spanish)

En este artículo, presentamos una nueva clase de mapeos α -nonexpansivos generalizados de Bregman en términos de la distancia de Bregman. Establecemos varios teoremas de convergencia débiles y fuertes de los esquemas iterativos de Ishikawa y Noor para mapeos α -nonexpansivos generalizados de Bregman en espacios de Banach. Se da un ejemplo numérico para ilustrar los principales resultados de la aproximación de punto fijo utilizando el algoritmo de Halpern.

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Additional details

Additional titles

Translated title (Arabic)
تقريب النقاط الثابتة لتعيينات بريغمان المعممة α - غير الموسعة
Translated title (French)
Approximation des points fixes des mappages α-non expansifs généralisés de Bregman
Translated title (Spanish)
Aproximación de puntos fijos de mapeos α-nonexpansivos generalizados de Bregman

Identifiers

Other
https://openalex.org/W2966051666
DOI
10.3390/math7080709

Is supplement to
https://openalex.org/W4206321257 (Other)
https://openalex.org/W2883505870 (Other)
https://openalex.org/W2755632338 (Other)
https://openalex.org/W2363849453 (Other)
https://openalex.org/W2361703941 (Other)
https://openalex.org/W2347090672 (Other)
https://openalex.org/W2091172514 (Other)
https://openalex.org/W2090682043 (Other)
https://openalex.org/W2053619914 (Other)
https://openalex.org/W1975728083 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Thailand

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