On modular firmly nonexpansive mappings in the variable exponent sequence spaces $$\ell _{p(\cdot )}$$

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Afrah A. N. Abdou ◽  
M. A. Khamsi
Keyword(s):  
Variable Exponent ◽  
Nonexpansive Mappings ◽  
Sequence Spaces ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings

scholarly journals Periodic Points of Modular Firmly Mappings in the Variable Exponent Sequence Spaces ℓp(·)

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2418
Author(s):  
Afrah A. N. Abdou ◽  
Mohamed A. Khamsi
Keyword(s):  
Variable Exponent ◽  
Nonexpansive Mappings ◽  
Periodic Points ◽  
Sequence Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Firmly Nonexpansive ◽  
Nonconvex Domains

In this work, we investigate the existence of periodic points of mappings defined on nonconvex domains within the variable exponent sequence spaces ℓp(·). In particular, we consider the case of modular firmly nonexpansive and modular firmly asymptotically nonexpansive mappings. These kinds of results have never been obtained before.

Shrinking projection methods for firmly nonexpansive mappings

2009 ◽  
Vol 71 (12) ◽  
pp. e1626-e1632 ◽  
Author(s):  
Koji Aoyama ◽  
Fumiaki Kohsaka ◽  
Wataru Takahashi
Keyword(s):  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Shrinking Projection Methods

scholarly journals Quantitative analysis of a subgradient-type method for equilibrium problems

2021 ◽  
Author(s):  
Nicholas Pischke ◽  
Ulrich Kohlenbach
Keyword(s):  
Quantitative Analysis ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Metric Regularity ◽  
Rates Of Convergence ◽  
Type Method ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings ◽  
Fixed Point Sets

AbstractWe use techniques originating from the subdiscipline of mathematical logic called ‘proof mining’ to provide rates of metastability and—under a metric regularity assumption—rates of convergence for a subgradient-type algorithm solving the equilibrium problem in convex optimization over fixed-point sets of firmly nonexpansive mappings. The algorithm is due to H. Iiduka and I. Yamada who in 2009 gave a noneffective proof of its convergence. This case study illustrates the applicability of the logic-based abstract quantitative analysis of general forms of Fejér monotonicity as given by the second author in previous papers.

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