On the Existence of Weakly Continuous Solutions of the Nonlinear Functional Equations and Functional Differential Equations in Reflexive and Nonreflexive Banach Spaces
Автор(ы):
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
Аннотация:
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
Ключевые слова
- fixed point theorem
- functional equation
- measure of weak noncompactness
- Weak solution
Ссылки:
- J. M. Ball, Weak continuity properties of mapping and semi-groups, Proc. Royal Soc. Edinbourgh Sect. A, 72 (1973-1974), 275-280
- M. Cichon, Weak solutions of ordinary differential equations in Banach spaces, Discuss. Math. Differ. Incl. Control Optim., 15 (1995), 5-14
- M. Cichon, I. Kubiaczyk, Existence theorem for the Hammerstein integral equation, Discuss. Math. Differ. Incl. Control Optim., 16(2) (1996), 171-177
- F. S. De Blasi, On a property of the unit sphere in Banach spaces, Bull. Math. Sot. Sci. Math. Roum. 21(1977)259-262
- A. M. A. El-Sayed, H. H. G. Hashem, Weak maximal and minimal solutions for Hammerstein andUrysohn integral equations in reflexive Banach spaces, Differential Equation and Control Processes, No. 4(2008), 50-62
- I. Kubiaczyk, On a fixed point theorem for weakly sequentially continuous mapping. Discuss. Math., Differ. Incl. 15(1995)15-20
- W. J. Knight, Solutions of differential equations in B-spaces, Duke Math. J. 41 (1974), 437-442
- D. O'Regan, Integral equations in reflexive Banach spaces and weak topologies, Amer. Math. Soc., Vol. 124, No. 2, (1996), 607-614
- D. O'Regan, Fixed point theory for weakly sequentially continuous mapping, Math. Comput. Modeling, 27 (1998), 1-14
- D. O'Regan, Weak solutions of ordinary differential equations in Banach spaces, Appl. Math. Lett. 12 (1999), 101-105
- W. Rubin, Functional Analysis, McGraw-Hill, Inc. New York, Harlow, (1991. (
- H. A. H. Salem, A. M. A. El-Sayed, Fractional order integral equations in reflexive Banach spaces, Math. Slovaca, 55 , No. 2 (2005), 169-181
