Mixed equilibrium and fixed point problems for a countable family of multi-valued Bregman quasi-nonexpansive mappings in reflexive Banach space

2021 ◽  
Vol Accepted ◽  
Author(s):  
Oluwatosin Temitope Mewomo ◽  
Hammed Anuoluwapo Abass ◽  
Chinedu Izuchukwu ◽  
Grace Nnennaya Ogwo ◽  
Olawale Kazeem Oyewole
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Reflexive Banach Space ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Countable Family ◽  
Mixed Equilibrium

scholarly journals Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xianbing Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Bounded Sets

It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.

scholarly journals c0 can be renormed to have the fixed point property for affine nonexpansive mappings

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5645-5663 ◽  
Author(s):  
Veysel Nezir ◽  
Nizami Mustafa
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Reflexive Banach Space ◽  
Nonexpansive Mappings ◽  
Equivalent Norm ◽  
Positive Answer ◽  
Fixed Point Property ◽  
Null Sequence ◽  
Point Property ◽  
Usual Norm

P.K. Lin gave the first example of a non-reflexive Banach space (X,||?||) with the fixed point property (FPP) for nonexpansive mappings and showed this fact for (l1,||?||1) with the equivalent norm ||?|| given by ||x|| = sup k?N 8k/1+8k ?1,n=k |xn|, for all x = (xn)n?N ? l1. We wonder (c0, ||?||1) analogue of P.K. Lin?s work and we give positive answer if functions are affine nonexpansive. In our work, for x = (?k)k ? c0, we define |||x||| := lim p?? sup ?k?N ?k (?1,j=k |?j|p/2j)1/p where ?k ?k 3, k is strictly increasing with ?k > 2, ?k ? N, then we prove that (c0,|||?|||) has the fixed point property for affine |||?|||-nonexpansive self-mappings. Next, we generalize this result and show that if ?(?) is an equivalent norm to the usual norm on c0 such that lim sup n ?(1/n ?n,m=1 xm + x) = lim sup n ?(1/n ?n,m=1 xm) + ?(x) for every weakly null sequence (xn)n and for all x ? c0, then for every ? > 0, c0 with the norm ||?||? = ?(?)+?|||?||| has the FPP for affine ||?||?-nonexpansive self-mappings.

scholarly journals A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1487-1497
Author(s):  
Sun Cho
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Reflexive Banach Space ◽  
Fixed Point Problems ◽  
Projection Algorithm ◽  
Reflexive Banach Spaces

In this paper, a monotone Bregan projection algorithm is investigated for solving equilibrium problems and common fixed point problems of a family of closed multi-valued Bregman quasi-strict pseudocontractions. Strong convergence is guaranteed in the framework of reflexive Banach spaces.

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