On the Existence of Weakly Continuous Solutions of the Nonlinear Functional Equations and Functional Differential Equations in Reflexive and Nonreflexive Banach Spaces
Author(s):
A.M.A. El-Sayed
Faculty of Science,
Alexandria University,
Alexandria,
Egypt
amasayed@alexu.edu.eg
W.G. El-Sayed
Faculty of Science,
Alexandria University,
Alexandria,
Egypt
wagdygoma@alexu.edu.eg
A. A. H. Abd El-Mowla
Faculty of Science,
Omar Al-Mukhtar University,
Derna, Libya
Abstract:
The existence of solution of the functional equations and functional integral and
differential equations, in different spaces of functions, have been s
tudied by some authors. Here, we are concerned with an initial
value problem of the nonlinear functional differential equation
and present two theorems for the existence of at least one weak solution
for this functional differential equation in the reflexive and nonreflexive Banach
spaces relative to the weak topology.
For this aim we study, firstly, the existence of weakly continuous solutions
for a nonlinear functional equation
in the reflexive and nonreflexive Banach spaces
Keywords
- fixed point theorem
- functional equation
- measure of weak noncompactness
- Weak solution
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