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1

Starlikeness and convexity of certain integral operators defined by convolution

Aggarwal J., Mathur R.

Journal of Mathematics and Applications

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2015

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Vol. 38

5--13

EN

We define two new general integral operators for certain analytic functions in the unit disc U and give some sufficient conditions for these integral operators on some subclasses of analytic functions.

2

Certain classes of multivalent functions with negative coefficients involving the Hadamard product

Juma A. R. S.

Journal of Applied Analysis

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2012

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Vol. 18, nr 1

133-143

EN

In this paper, we introduce and investigate a new class of multivalent functions by using the Hadamard product structure defined in the open unit disk. We obtain coefficient estimates, a distortion theorem, extreme points and criteria of starlikeness and convexity for functions which belong to our class. Relevant connections of the results with those obtained in earlier works are also pointed out.

3

Certain subclass of multivalent functions involving the Cho-Kwon-Srivastava operator

Zeng T., Gao Ch-Y., Wang Z-G., Aghalary R.

Journal of Mathematics and Applications

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2008

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Vol. 30

161-170

EN

In the present paper, we introduce a new subclass S(sup (j)) (sub p, λ) (α; a, c; φ) of multivalent functions involving the Cho-Kwon-Srivastava operator. Such results as inclusion relationships, coefficient estimates and convolution properties for this class are proved. The results presented here would provide extensions of those given in earlier works.

4

Certain classes of multivalent functions with negative coefficients defined by using a differential operator

Aouf M. K.

Journal of Mathematics and Applications

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2008

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Vol. 30

5-21

EN

In this paper, we investigate the various important prop-erties and characteristics of the subclasses Sn (p, q, α, β) and Cn (p, q, α, β) of multivalent functions with negative coefficients defined by using a differential operator. We also derive many results for the modified Hadamard products of functions belongingto the classes Sn(p, q, α, β) and Cn(p, q, α, β). Finally several applications involving an integral operator and certain fractional calculus operators are also considered.

5

Some inequalities involving differential operators and their applications to certain multivalent functions

Dziok J., Huseyin I., Piejko K.

Journal of Mathematics and Applications

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2007

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Vol. 29

109-120

EN

The main object of the present paper is to investigate several results of certain differential operators which were recently introduced and (or) studied in a series of papers by Chen et et al. [1-3], Irmak et al. [8, 10, 11], Dziok et al. [5, 6] and Liu et al. [14]. In addition, some applications of our results involving certain differential inequalities of multivalently analytic and (or) multivalently raeromorphic functions are given. Our certain results also include some recent results in [5, 6, 9, 11, 12].