SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH SALAGEAN DERIVATIVE

In the present paper a new subclass of Harmonic univalent functions is defined using Salegaon derivative operator and several interesting properties like coefficient bound, distortion theorem are obtained. 2000 Mathematics Subject Classification:30C45,30C55

INCLUSION AND NEIGHBORHOOD PROPERTIES OF A CERTAIN SUBCLASSES OF P-VALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

By means of Ruscheweyh derivative operator, we introduced and investigated two new subclasses of p-valent analytic functions.The various results obtained here for each of these function class include coefficient bounds and distortion inequalities, associated inclusion relations for the (n, θ)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of non-homogenous differential equation. 1 Introductin Let Tp(n) denote the class of functions of the form: f(z) = z p ∞∑ − akz k k=n+p (ak ≥ 0; p, n ∈ N = {1, 2,....}), (1.1) which are analytic and p-valent in the open unit disc U = {z: |z | < 1}. The modified Hadamard product (or convolution) of the function f(z) given by (1.1) and the function g(z) ∈ Tp(n) given by g(z) = z p ∞∑ − bkz k k=n+p (bk ≥ 0; p, n ∈ N) (1.2) is defined by (f ∗ g)(z) = z p ∞∑ − akbkz k = (g ∗ f)(z). (1.3) k=n+

DOI 10.1007/s10270-010-0155-y

Non-functional properties in the model-driven development of service-oriented system