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We first present two classes ζ q n ( α , η ) and ℑ q n ( α , η ) of complex order bounded q − starlike and q − convex univalent functions using the salagean q − derivative operator D q n f ( z ) that is defined in ∇ = { z ∈ C : | z | < 1 } . In such classes, we also analyze the convolution properties, inclusion properties, and estimates of coefficients.

In this paper, a numerical solution of population dynamics of human immunodeficiency type 1 virus (HIV-1) model is considered by using Legendre spectral-collocation method. The computed results given here are compared with previous works to show efficiency of the proposed method.

In this paper we derive some results for certain new class of analytic functions defined by using Ruscheweyh derivative with varying arguments.

R. M. EL-Ashwah Department of Mathematics, Faculty of Science, University of Damietta New Damietta 34517, Egypt. e-mail: r_elashwah@yahoo.com M. K. Aouf Department of Mathematics, Faculty of Science, University of Mansoura Mansoura 35516, Egypt. e-mail: mkaouf127@yahoo.com F. M. Abdulkarem Department of Mathematics, Faculty of Science, University of Damietta New Damietta 34517, Egypt. e-mail: fammari76@gmail.com

In this paper, we de…ne a generalized class of starlike functions de…ned by convolution with negative coe¢cients and obtain some geometric properties for this class such as coe¢cient estimates, distortion theorems, radii of close-to-convexity, starlikeness and convexity, closure theorems and extreme points. Further we obtain modi…ed Hadamard produt, for functions belonging to this class.

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

We introduce certain new classesκ−VST(α,β)andκ−VUCV(α,β), which represent theκuniformly starlike functions of orderαand typeβwith varying arguments and theκuniformly convex functions of orderαand typeβwith varying arguments, respectively. Moreover, we give coefficients estimates, distortion theorems, and extreme points of these classes.

We introduce a class of multivalent -uniformly functions with varying arguments, give some properties of functions in this class, and obtain sharp results including coefficient estimates and distortion theorems. Finally, we give the extreme points for this class.