Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application

被引：4
|
作者：
Beg, Ismat [1 ]
Abbas, Mujahid [2 ,3 ]
Asghar, Muhammad Waseem [2 ]
机构：
[1] Lahore Sch Econ, Dept Math & Stat Sci, Lahore 53200, Pakistan
[2] Govt Coll Univ, Dept Math, Lahore 54000, Pakistan
[3] China Med Univ, Dept Med Res, Taichung 40402, Taiwan
来源：
MATHEMATICS | 2022年 / 10卷 / 22期
关键词：
AA-iteration; generalized alpha-nonexpansive mapping; fixed point; Banach space; APPROXIMATING FIXED-POINTS; THEOREMS; WEAK;
D O I：
10.3390/math10224375
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The aim of this paper is to approximate the fixed points of generalized alpha-nonexpansive mappings using AA-iterative algorithm. We establish some weak and strong convergence results for generalized alpha-nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the AA-iterative algorithm converges faster than some others algorithms for generalized alpha-nonexpansive mappings. Lastly, using the AA-iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra-Stieltjes type.
引用
收藏
页数：16
相关论文
共 50 条
  • [21] Comment on "A Strong Convergence of a Generalized Iterative Method for Semigroups of Nonexpansive Mappings in Hilbert Spaces"
    Farman Golkarmanesh
    Saber Naseri
    Fixed Point Theory and Applications, 2011
  • [22] Convergence of Iterative Process for Generalized I-Asymptotically Quasi-Nonexpansive Mappings
    Temir, Seyit
    THAI JOURNAL OF MATHEMATICS, 2009, 7 (02): : 367 - 379
  • [23] Convergence of RK-iterative process for generalized nonexpansive mappings in CAT(0) spaces
    Ritika
    Khan, Safeer Hussain
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2019, 12 (05)
  • [24] A NEW ITERATIVE ALGORITHM FOR APPROXIMATION OF FIXED POINTS OF MULTIVALUED GENERALIZED α-NONEXPANSIVE MAPPINGS
    Abbas, Mujahid
    Iqbal, Hira
    Yao, Jen-Chih
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2021, 22 (03) : 471 - 486
  • [25] An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings
    Agarwal, Ravi P.
    Qin, Xiaolong
    Kang, Shin Min
    FIXED POINT THEORY AND APPLICATIONS, 2011, : 1 - 17
  • [26] An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings
    Ravi P Agarwal
    Xiaolong Qin
    Shin Min Kang
    Fixed Point Theory and Applications, 2011
  • [27] STRONG CONVERGENCE OF COMPOSITE ITERATIVE METHODS FOR NONEXPANSIVE MAPPINGS
    Jung, Jong Soo
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (06) : 1151 - 1164
  • [28] Convergence of path and an iterative method for families of nonexpansive mappings
    Chidume, Charles Dike
    Ali, Bashir
    APPLICABLE ANALYSIS, 2008, 87 (01) : 117 - 129
  • [29] Iterative Algorithm and Δ-Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces
    Tang, J. F.
    Chang, S. S.
    Lee, H. W. Joseph
    Chan, C. K.
    ABSTRACT AND APPLIED ANALYSIS, 2012,
  • [30] Ishikawa's Iterative Algorithm of Nonexpansive Mappings and Averaged Mappings
    Duan Qibin
    Wang Erli
    Wu Dingping
    Xie Xuping
    PROCEEDINGS OF THE 2012 INTERNATIONAL CONFERENCE ON COMMUNICATION, ELECTRONICS AND AUTOMATION ENGINEERING, 2013, 181 : 689 - 695
12345