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Keywords
(5)
Asymptotic Stability
banach space
Fixed Point Theorem
Functional Integration
measure of noncompactness
Related Publications
(1)
An application of a measure of noncompactness in the study of asymptotic stability
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LOCAL ASYMPTOTIC STABILITY FOR NONLINEAR QUADRATIC FUNCTIONAL INTEGRAL EQUATIONS
LOCAL ASYMPTOTIC STABILITY FOR NONLINEAR QUADRATIC FUNCTIONAL INTEGRAL EQUATIONS,Bapurao C. Dhage,S. S. Bellale
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LOCAL ASYMPTOTIC STABILITY FOR NONLINEAR QUADRATIC FUNCTIONAL INTEGRAL EQUATIONS
(
Citations: 2
)
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Bapurao C. Dhage
,
S. S. Bellale
In the present study, using the characterizations of measures of noncompactness we prove a theorem on the existence and local
asymptotic stability
of solutions for a quadratic functional
integral equation
via a
fixed point theorem
of Darbo. The investigations are placed in the
Banach space
of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of abstract result presented in the paper.
Published in 2008.
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Citation Context
(1)
...Let us mention that the concept of attractivity of solutions was introduced in Hu and Yan [9] and Banas and Rzepka [3] while the concept of asymptotic attractivity is introduced in Dhage [
7
]...
Bapurao C. Dhage
,
et al.
LOCAL ASYMPTOTIC STABILITY FOR NONLINEAR QUADRATIC FUNCTIONAL INTEGRAL...
References
(5)
Measure of noncompactness in Banach spaces
(
Citations: 41
)
J. Bana S
,
K. Goebel
Published in 1980.
An application of a measure of noncompactness in the study of asymptotic stability
(
Citations: 19
)
J. Banas
,
B. Rzepka
Journal:
Applied Mathematics Letters
, vol. 16, no. 1, pp. 16, 2003
Fixed points and stability of an integral equation: nonuniqueness
(
Citations: 19
)
T. A. Burton
,
Bo Zhang
Journal:
Applied Mathematics Letters
, vol. 17, no. 7, pp. 839846, 2004
LOCAL ASYMPTOTIC STABILITY FOR NONLINEAR QUADRATIC FUNCTIONAL INTEGRAL EQUATIONS
(
Citations: 2
)
Bapurao C. Dhage
,
S. S. Bellale
Published in 2008.
The global attractivity and asymptotic stability of solution of a nonlinear integral equation
(
Citations: 18
)
Xiaoling Hu
,
Jurang Yan
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 321, no. 1, pp. 147156, 2006
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Citations
(2)
LOCAL ASYMPTOTIC STABILITY FOR NONLINEAR QUADRATIC FUNCTIONAL INTEGRAL EQUATIONS
(
Citations: 2
)
Bapurao C. Dhage
,
S. S. Bellale
Published in 2008.
ATTRACTIVITY AND POSITIVITY RESULTS FOR NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS VIA MEASURE OF NONCOMPACTNESS
(
Citations: 1
)
BAPURAO C. DHAGE