Cosine families of operators in a class of Fréchet spaces

We consider a class of impulsive neutral second-order stochastic functional evolution equations. The Sadovskii fixed point theorem and the theory of strongly continuous cosine families of operators are used to investigate the sufficient conditions for the controllability of the system considered. An example is provided to illustrate our results.

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Existence of Solutions of a Class of Abstract Second Order Nonlinear Integrodifferential Equations

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953302000126 ◽

2002 ◽

Vol 15 (2) ◽

pp. 115-124 ◽

Cited By ~ 3

Author(s):

K. Balachandran ◽

J. Y. Park

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Banach Spaces ◽

Point Theorem ◽

Existence Of Solutions ◽

Second Order ◽

Integrodifferential Equations ◽

Cosine Families ◽

Schaefer Fixed Point Theorem ◽

Families Of Operators

In this paper we prove the existence of solutions of nonlinear second order integrodifferential equations in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of operators and the Schaefer fixed point theorem.

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Distributionally chaotic families of operators on Fréchet spaces

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2016022 ◽

2016 ◽

Vol 15 (5) ◽

pp. 1915-1939 ◽

Cited By ~ 8

Author(s):

Marina Murillo-Arcila ◽

Pedro J. Miana ◽

Marko Kostić ◽

J. Alberto Conejero

Keyword(s):

Fréchet Spaces ◽

Families Of Operators

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Conformable Fractional Cosine Families of Operators

Journal of Mathematical Sciences and Modelling ◽

10.33187/jmsm.435481 ◽

2019 ◽

pp. 112-116

Author(s):

Elomari M'hamed

Keyword(s):

Cosine Families ◽

Families Of Operators

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Measure of noncompactness and semilinear differential equations in Fréchet spaces

Tbilisi Mathematical Journal ◽

10.32513/tbilisi/1553565627 ◽

2019 ◽

Vol 12 (1) ◽

pp. 69-81 ◽

Cited By ~ 1

Author(s):

Amaria Arara ◽

Mouffak Benchohra ◽

Fatima Mesri

Keyword(s):

Differential Equations ◽

Measure Of Noncompactness ◽

Fréchet Spaces

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Common Fixed Point and Invariant Approximation Results on Non-Starshaped Domains

Georgian Mathematical Journal ◽

10.1515/gmj.2005.659 ◽

2005 ◽

Vol 12 (4) ◽

pp. 659-669

Author(s):

Nawab Hussain ◽

Donal O'Regan ◽

Ravi P. Agarwal

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Fréchet Spaces ◽

Approximation Theorems ◽

Type Approximation ◽

Invariant Approximation ◽

Commuting Maps

Abstract We extend the concept of 𝑅-subweakly commuting maps due to Shahzad [J. Math. Anal. Appl. 257: 39–45, 2001] to the case of non-starshaped domains and obtain common fixed point results for this class of maps on non-starshaped domains in the setup of Fréchet spaces. As applications, we establish Brosowski–Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa and Shahzad.

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Existence results for some integro-differential equations with state-dependent nonlocal conditions in Fréchet Spaces

Nonautonomous Dynamical Systems ◽

10.1515/msds-2020-0121 ◽

2020 ◽

Vol 7 (1) ◽

pp. 272-280

Author(s):

Mamadou Abdoul Diop ◽

Kora Hafiz Bete ◽

Reine Kakpo ◽

Carlos Ogouyandjou

Keyword(s):

Differential Equations ◽

Resolvent Operator ◽

Mild Solutions ◽

Linear Part ◽

Nonlocal Conditions ◽

Existence Results ◽

Fréchet Spaces ◽

Local Conditions ◽

State Dependent ◽

Darbo Fixed Point Theorem

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

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