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On fixed point results for a class of generalized mean nonexpansive mappings


Abstract

In this paper, we introduce a new class of generalized mean nonexpansive mappings and propose an iterative algorithm for approximating the fixed points of this class of mappings in the frame work of uniformly convex Banach spaces. We establish some fixed point results for this class of mappings and prove the convergence of the propose iterative algorithm. Finally, numerical experiment is presented to demonstrate the efficiency of our algorithm in comparison with other existing algorithms in literature.

Вводиться новий клас узагальнених нерозтягуючих у середньому відображень, для яких пропонується ітераційний алгоритм наближеного знаходження нерухомих точок в контексті рівномірно опуклих банахових просторів. Для цього класу відображень доведені теореми про нерухому точку, а також збіжність зазначеного алгоритму. Шляхом чисельного експерименту наш алгоритм порівнюється з відомими.

Key words: Generalized mean nonexpansive mappings; fixed point; new iterative scheme; strong and weak convergence theorems.


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Article Information

TitleOn fixed point results for a class of generalized mean nonexpansive mappings
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 4, 356-372
DOI10.31392/MFAT-npu26_4.2020.07
MilestonesReeived 30/07/2019; Revised 31/10/2020
CopyrightThe Author(s) 2020 (CC BY-SA)

Authors Information

A. A. Mebawondu
Shool of Mathematis, Statistis and Computer Siene, University of KwaZulu-Natal, Durban, South Afria

C. Izuchukwu
Shool of Mathematis, Statistis and Computer Siene, University of KwaZulu-Natal, Durban, South Afria

K. O. Oyewole

O. T. Mewomo


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Citation Example

A. A. Mebawondu, C. Izuchukwu, K. O. Oyewole, and O. T. Mewomo, On fixed point results for a class of generalized mean nonexpansive mappings, Methods Funct. Anal. Topology 26 (2020), no. 4, 356-372.


BibTex

@article {MFAT1451,
    AUTHOR = {A. A. Mebawondu and C. Izuchukwu and K. O. Oyewole and O. T. Mewomo},
     TITLE = {On fixed point results for a class of generalized mean nonexpansive mappings},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {26},
      YEAR = {2020},
    NUMBER = {4},
     PAGES = {356-372},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_4.2020.07},
       URL = {http://mfat.imath.kiev.ua/article/?id=1451},
}


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