f(z)∗ψ(z) In this paper, we determine sharp lower bounds for Re Re fn(z)∗ψ(z) f(z)∗ψ(z) and fn(z)∗ψ(z). We extend the results of ([1] – [5]) and correct the conditions for the results of Frasin [2, Theorem 2.7], [1, Theorem 2], Rosy et al. [4, Theorems 4.2 and 4.3], as well as Raina and Bansal [3, Theorem 6.2].

topology is λ multiplier convergent in the orig-inal topology of the space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. How-ever, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial

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ABSTRACT. In the present paper we give some results concerning partial sums of certain meromorphic functions.We also consider the partial sums of certain integral operator.

Abstract. The object of the present paper is to consider of starlikeness and convexity of partial sums of certain analytic functions in the open unit disk 1

This paper introduces an efficient method for the maintenance of wavelet-based histograms built on partial sums. Wavelet-based histograms can be constructed from either raw data distributions or partial sums. The two construction methods have their own merits. Previous works have only focused

ABSTRACT. We determine conditions under which the partial sums of the Libera integral operator of functions of bounded turning are also of bounded turning.

The partial sums f3(z) of some extermal functions for various classes S ∗ , K and R of starlike functions, convex functions and functions with positive real part in the open unit disk U, respectively, are discussed. In general, the partial sums can not preserve the same character as the initial

We present a data structure that allows to maintain in logarithmic time all partial sums of elements of a linear array during incremental changes of element’s values. Key words: Partial sums; Data structures; Algorithms 1

1 Introduction The central theme of this paper is the complexity of the partial-sum problem: Given a d-dimensional array A with n entries in a semigroup and a d-rectangle q = [a1; b1] \Theta \Delta \Delta \Delta \Theta [ad; bd], compute the sum oe(A; q) = X