On connectivity points of Darboux functions
Jan M. Jastrzębski, Jacek M. Jędrzejewski (1989)
Mathematica Slovaca
Pawlak, R.J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
T. Zgraja (2005)
Acta Universitatis Carolinae. Mathematica et Physica
Michael J. Evans (1974)
Colloquium Mathematicae
Masayoshi Hata (1988)
Annales de l'institut Fourier
We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham’s functional equations. Then we show that for any
Ladislav Mišík (1984)
Mathematica Slovaca
Gy. Muszely (1973)
Metrika
Małgorzata Klimek (2011)
Banach Center Publications
One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
Supriya Pal, Dilip Kumar Ganguly, Lee Peng Yee (2005)
Mathematica Slovaca
Akgün, Ramazan, Kokilashvili, Vakhtang (2011)
Banach Journal of Mathematical Analysis [electronic only]
J. Smital (1976)
Aequationes mathematicae
J. Smital (1976)
Aequationes mathematicae
Kazimierz Nikodem (1980)
Aequationes mathematicae
Jiří Jarník (1973)
Časopis pro pěstování matematiky
Jack Ceder (1976)
Fundamenta Mathematicae
J. Smital (1989)
Aequationes mathematicae
Kirill Naralenkov (2010)
Czechoslovak Mathematical Journal
In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
José Gámez, José Mendoza (1998)
Studia Mathematica
The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...
Powa̧zka, Zbigniew, Rose, Michael (1994)
Mathematica Pannonica
A. van Rooij, W. Schikhof (1988)
Fundamenta Mathematicae