An Existence Theorem of Solutions of Semilinear Equations in Reflexive Banach Spaces and Its Applications

1993 ◽  
Vol 4 (7) ◽  
pp. 317-330 ◽  
Author(s):  
Chun-Lei Tang
Keyword(s):  
Existence Theorem ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Semilinear Equations

scholarly journals Approximating Fixed Points of The General Asymptotic Set Valued Mappings

2020 ◽  
Vol 18 ◽  
pp. 52-59
Author(s):  
Salwa Salman Abed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Set Valued Mapping ◽  
Set Valued Mappings ◽  
Fixed Point Iterative Method

  The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping  and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by  yn+1 = tn z+ (1-tn )un ,  un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces.  As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

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