We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential equations...
We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.
Let f(z), , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values and the iterated mean values of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).
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In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...
La nozione di trasformazione proiettiva già nota per gli spazi riemanniani ricorrenti rispetto al tensore di curvatura o a quello di Ricci viene estesa agli spazi di Finsler con analoghe proprietà.
In questa Nota vengono considerate le congruenze geodetiche di uno spazio di Finsler.
Hayden [1] ha studiato le linee asintotiche di ordine p in un sottospazio di uno spazio riemanniano ed ha ottenuto una espressione per la curvatura in qualsiasi punto di una linea asintotica di massimo ordine. In questo lavoro gli Autori hanno voluto studiare le medesime proprietà per una ipersuperficie di uno spazio di Finsler.
A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.
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