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Displaying similar documents to “On integrals of functions with values in a complete linear metric spaces”

On integrability in F-spaces

Mikhail Popov (1994)

Studia Mathematica

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Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable l p -valued function (0 < p < 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence...

Analytic solutions of a second-order functional differential equation with a state derivative dependent delay

Jian-Guo Si, Xin-Ping Wang (1999)

Colloquium Mathematicae

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This paper is concerned with a second-order functional differential equation of the form x ' ' ( z ) = x ( a z + b x ' ( z ) ) with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.