Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Demonstratio Mathematica

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Cauchy-Schwarz inequality

Sortuj według:

Ogranicz wyniki do:

On some consequences of the functional generalization of the parallelogram identity

Mączyński M. M.

Demonstratio Mathematica

2014

Vol. 47, nr 2

493--506

The aim of this paper is to unify the partial results, which up to now, have been dispersed in various publications in order to show the importance of the functional form of parallelogram identity in mathematics and physics. We study vector spaces admitting a real non-negative functional which satisfies an identity analogous to the parallelogram identity in normed vector spaces. We show that this generalized parallelogram identity also implies an equality analogous to the Cauchy–Schwarz inequality. We study the consequences of this identity in real and complex vector spaces, in generalized Riesz spaces and in abelian groups. We give a physical interpretation to these results. For vector spaces of observables and states, we show that the parallelogram identity implies an inequality analogous to Heisenberg’s uncertainty principle (HUP), and we show that we can obtain the standard structure of quantum mechanics from the parallelogram identity, without assuming from the beginning the HUP. The role of complex numbers in quantum mechanics is discussed.

A note on the abstract Cauchy-Kovalevskaya theorem

Ghisi M.

Demonstratio Mathematica

1999

Vol. 32, nr 2

331-343

We give a version of the abstract Cauchy-Kovalevskaya Theorem for the Cauchy problem u'= A(t, u), u(O)=u0 when A is not necessarily a Lipschitz continuous operator. The operator A(t,u)= F(t,u,u) verifies 1) F:1 I x Br1,R x Br,R- X3 for s < r < ro (r1 < ro is fixed), F(t, u, .) is Lipschitz continuous, and F(t, ., ,) is alpha-Lipshitz continuous or 2 ) F : I x Br1 , R x X r - X 9 for s< r < ro (r1 < ro is fixed), and F(t, ., .) is alpha-Lipschitz continuous , where Br,R denotes the ball of radius R in Xr. We prove the result by using Tonelli approximations and fixed point theorems.

A certain subclass of analytic p-valent functions with negative coefficients

Aouf M., Hossen H., Srivastava H.

Demonstratio Mathematica

1998

Vol. 31, nr 3

595-608

The object of the present paper is to derive several sharp results for the modified Hadamard products (or convolution) of functions belonging to a certain subclass Gp (lambda,alfa) of analytic and p-valent functions with negative coefficients, which is related rather closely to a class Fp (lambda,alfa) studied earlier by Lee et al. [4] . Distortion theorems for the fractional calculus (that is, fractional integral and fractional derivative) of functions in the class Gp (lambda,alfa) are obtained. This paper is essentially a sequel to the work of Aouf [3] who introduced, and derived some basic properties of, the class Gp(lambda,alfa).