A new look at q-hypergeometric functions

For complex parameters ai, bj , q(i = 1, ..., r, j = 1, ..., s, bj ∈ C\{0, −1, −2, ...}, |q| < 1), define the q-hypergeometric function rΦs(a1, ..., ar; b1, ..., bs; q, z) by rΦs(ai; bj ; q, z) = ∑∞ n=0 (a1, q)n...(ar, q)n (q, q)n(b1, q)n...(bs, q)n z n (r = s + 1; r, s ∈ N0 = N ∪ {0}; z ∈ U) where N denote the set of positive integers and (a, q)n is the q-shifted factorial defined by (a, q)n = { 1, n = 0; (1 − a)(1 − aq)(1 − aq2)...(1 − aqn−1), n ∈ N. Recently, the authors [7] defined the linear operator M(ai, bj ; q)f. Using the operatör M(ai, bj ; q)f(z)f, Aldweby and Darus [13] gave a new integral operator. In this work we highlight a result related to the new integral operator.Publisher's Versio

On certain classes of meromorphic harmonic concave functions defined by al-Oboudi operator

In this work, a class of meromorphic harmonic concave functions defined by Oboudi operator in the punctured unit disc is introduced. Coefficient conditions, distortion inequalities, extreme points, convolution bounds, geometric convolution, integral convolution and convex combinations for functions f belonging to this class are obtained

On a certain subclass of meromorphic univalent functions with fixed second positive coefficients

In the present paper, we consider the subclass of meromorphic univalent functions S<SUB>p</SUB><SUP>*</SUP>[k,α,β,c] with fixed second positive coefficient. The object of the present paper is to show coefficient estimates, onvex liner combinations, some distortion theorems, and redii of star likeness and convexity for f(z) in the class S<SUB>p</SUB><SUP>*</SUP>[k,α,β,c]

Inclusion Properties on a Class of Meromorphic Functions Defined by a Linear Operator

In the present paper, we study a certain class of meromorphic univalent functions f(z) dened by the linear operator L(α,β) f (z). The aim of the present paper is to prove some properties for the class Σα,β,kλ;(h) to satisfy the certain subordination.AMS Subject Classication: 30C4

Univalence criteria of certain integral operator

In this paper, univalence criteria of certain integral operator defined by a generalised derivative operator is obtained

G-function Solutions for Diffusion and Laplace's equations

In this paper the Diffusion equation and Laplace's equation is solved by Modiffied separation of variables (MSV) method, suggested by Pishkoo and Darus . Using this method, Meijer's G-function solutions are derived in cylindrical coordinates system for two typical problems. These complex functions include all elementary functions and most of the special functions which are the solution of extensive problems in Physics and engineering

Second hankel determinant for a subclass of analytic functions involving Q-analogue of Ruscheweyh operator

Let S be the class of analytic functions which are univalent and normalised in the open unit disc :1 <.Uzz Second Hankel determinant of 2243aaa for a class of analytic functions involving q-analoque of Ruscheweyh operator is given

A Study on Becker's Univalence Criteria

We study univalence properties for certain subclasses of univalent functions K, K2, K3, and S(p), respectively. These subclasses are associated with a generalized integral operator. The extended Becker-typed univalence criteria will be studied for these subclasses