Some properties of generalized fundamentally nonexpansive mappings in Banach spaces

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Basic Sciences, Bu-Ali Sina University, Hamedan, Iran

Abstract

In this paper, we introduce a condition on mappings and show that the class of these mappings is broader than both the class of mappings satisfying condition (C) and the class of fundamentally nonexpansive mappings, and it is incomparable with the class of quasi-nonexpansive mappings and the class of mappings satisfying condition (L). Furthermore, we present some convergence theorems and fixed point theorems for mappings satisfying the condition in the setting of Banach spaces. Finally, an example is given to support the usefulness of our results.

Keywords

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[1] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed Point Theory for Lipschitzian-Type Mappings with Applications,
Springer, New York, 2009.
[2] S. Dhompongsa and N. Nanan, Fixed point theorems by ways of ultra-asymptotic centers, Abst. Appl. Anal. 2011
(2011) Article ID 826851.
[3] K. Goebel and W. A. Kirk, Iteration processes for nonexpansive mappings, Contemp. Math. 21 (1983) 115–123.
[4] J. Gar´ca-Falset, E. Llorens-Fuster and T. Suzuki, Fixed point theory for a class of generalized of nonexpansive
mappings, J. Math. Anal. Appl. 375 (2011) 115–123.
[5] E. Llorens-Fuster and E. Moreno-G´alvez, The fixed point theory for some generalized nonexpansive mappings,
Abst. Appl. Anal. 2011 (2011) Article ID 435686.
[6] M. Moosaei, On fixed point of fundamentally nonexpansive mappings in Banach spaces, Int. J. Nonlinear Anal.
Appl. 7(1) (2016) 219–224.
[7] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer.
Math. Soc. 73 (1976) 591–597.
[8] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math.
Anal. 340 (2008) 1088–10
Volume 12, Issue 2
November 2021
Pages 1343-1352
  • Receive Date: 12 December 2019
  • Accept Date: 28 September 2020