Nonlinear evolution equations in Banach spaces

1972 ◽  
Vol 11 (1) ◽  
pp. 57-94 ◽  
Author(s):  
M. G. Crandall ◽  
A. Pazy
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations

scholarly journals Convergence Theorems for Generalized Viscosity Explicit Methods for Nonexpansive Mappings in Banach Spaces and Some Applications

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 161
Author(s):  
Pongsakorn Sunthrayuth ◽  
Nuttapol Pakkaranang ◽  
Poom Kumam ◽  
Phatiphat Thounthong ◽  
Prasit Cholamjiak
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonexpansive Mappings ◽  
Nonlinear Evolution Equations ◽  
Fredholm Integral Equations ◽  
Explicit Method ◽  
Convergence Theorems ◽  
New Techniques ◽  
The Given

In this paper, we introduce a generalized viscosity explicit method (GVEM) for nonexpansive mappings in the setting of Banach spaces and, under some new techniques and mild assumptions on the control conditions, prove some strong convergence theorems for the proposed method, which converge to a fixed point of the given mapping and a solution of the variational inequality. As applications, we apply our main results to show the existence of fixed points of strict pseudo-contractions and periodic solutions of nonlinear evolution equations and Fredholm integral equations. Finally, we give some numerical examples to illustrate the efficiency and implementation of our method.

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