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Borel partitions of unity and lower Carathéodory multifunctions

S. Srivastava — 1995

Fundamenta Mathematicae

We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in A ( ( X ) ) 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...

On the mean values of an analytic function.

G. S. SrivastavaSunita Rani — 1992

Annales Polonici Mathematici

Let f(z), z = r e i θ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values I δ ( r ) and the iterated mean values N δ , k ( r ) 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).

Coefficient multipliers on spaces of vector-valued entire Dirichlet series

Sharma AkankshaGirja S. Srivastava — 2017

Mathematica Bohemica

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 X 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...

Asymptotic lines in a hypersurface of a Finsler space

S. C. SrivastavaR. S. Sinha — 1971

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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 k m 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.

Sets with doubleton sections, good sets and ergodic theory

A. KłopotowskiM. G. NadkarniH. SarbadhikariS. M. Srivastava — 2002

Fundamenta Mathematicae

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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