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Growth and Lδ-approximation of solutions of the Helmholtz equation in a finite disk

Kumar D, Basu A.

Journal of Applied Analysis

2014

Vol. 20, nr 2

119--128

In this paper we study the growth and Lδ-approximation, 1 ≤ δ ≤ ∞, of solutions (not necessarily entire) of Helmholtz-type equations. Moreover, we obtain the characterization of order and type of H ∈ HR, 0 < R < ∞, in terms of decay of approximation errors En(H,R0) and Ein,δ(H,R0), i = 1,2. Our results extend and improve the results obtained by McCoy [J. Approx. Theory 25 (1979), 153–168].

Statistical convergence on composite vector valued sequence space

Basu A., Srivastava P. D.

Journal of Mathematics and Applications

2007

Vol. 29

75-90

In this paper, we have defined the idea of statistical convergence and statistically Cauchy sequence over the generalized class of composite vector valued sequence space F(Ek, f). The class F(Ek, f) is in-troduced and discussed by Ghosh and Srivastava [7], where F is a normal paranormed sequence space, Ek's are Banach spaces and f is a modulus function. We have established some results of Fridy, Connor and Rath and Tripathy, such as, decomposition of statistically convergent sequences, equivalence of statistical convergence and statistical Cauchy convergence and sequentially completeness of the space of bounded statistically con-vergent sequences of F [E, f].