Attractive point and nonlinear ergodic theorems without convexity in reflexive Banach spaces

被引:0
作者
Bashir Ali
Lawal Yusuf Haruna
机构
[1] Bayero University,Department of Mathematical Sciences
[2] Kaduna State University,Department of Mathematical Sciences
来源
Rendiconti del Circolo Matematico di Palermo Series 2 | 2021年 / 70卷
关键词
Attractive point; Generalized hybrid mapping; Normally 2-generalized hybrid mapping; Generic 2-generalized nonspreading mapping; Generic 2-generalized Bregman nonspreading mapping; Primary 47H09; Secondary 47H25; 47J25;
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摘要
In this paper, we prove attractive point theorem for two commutative generic 2-generalized Bregman nonspreading mappings in reflexive Banach spaces. Also, a nonlinear ergodic theorem of Baillon type without convexity assumption on the aforementioned mappings is proved in the space. Our results improve and generalize many results announced recently in the literature.
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页码:1527 / 1540
页数:13
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  • [1] Ali B(2020)Iterative approximations of attractive point of a new generalized Bregman nonspreading mapping in Banach spaces Bull. Iran. Math. Soc. 46 331-354
  • [2] Haruna LY(2020)Fixed point approximations of noncommutative generic 2-generalized Bregman nonspreading mappings with equilibriums J. Nonlinear Sci. Appl. 13 303-316
  • [3] Ali B(2017)Existence theorems for attractive points of semigroups of Bregman generalized nonspreading mappings in Banach spaces Adv. Oper. Theory 2 257-268
  • [4] Haruna LY(2018)Weak and strong convergence theorems for commutative 2-generalized nonspreading mappings in Banach spaces J. Nonlinear Convex Anal. 2 345-364
  • [5] Ali B(1969)Gradient of convex functions Trans. Am. Math. Soc. 139 443-467
  • [6] Harbau MH(1975)Un theoreme de type ergodique pour less contractions nonlinears dans un espaces de Hilbert C. R. Acad. Sci. Paris Ser. A-B 280 1511-1541
  • [7] Yusuf LH(2001)Essentially smoothness, essentially strict convexity and Legendre functions in Banach space Commun. Contemp. Math. 3 615-647
  • [8] Alsulami SM(1967)The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming USSR Comput. Math. Math. Phys. 7 200-217
  • [9] Latif A(1981)An iterative row-action method interval convex programming J. Optim. Theory Appl. 34 321-353
  • [10] Takahashi W(2008)The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces Nonlinear Anal. 69 1402-1412