Certain classes of meromorphic multivalent functions

In this paper, we introduce and investigate two new classes of meromorphic multivalent functions. Such results as subordination properties, coefficient inequalities, convolution properties and integral representations are proved. Several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived.     

Neighborhoods of a new class of harmonic multivalent functions

We introduce and investigate a new subclass of harmonic multivalent functions defined by using a differential operator. We obtain coefficient conditions, distortion bounds, extreme points, convex combination for the above class of harmonic multivalent functions. We also, derive inclusion relationships involving the neighborhoods of harmonic multivalent functions.     

On neighborhoods of two new subclasses of multivalent functions with negative coefficients

In this paper, we introduce two new subclasses of p-valent analytic functions defined by means of fractional derivative of order δ. We obtained the various results including coefficient bounds and distortion inequalities for these function classes. Furthermore, we determine some inclusion relations for the (n,p,ε)-neighborhoods of a family of p-valent analytic functions with negative coefficients which is defined by means of a certain nonhomogeneous Cauchy-Euler differential equation.     

Some preserving subordination and superordination of analytic functions involving the Liu-Owa integral operator

In this paper, we obtain some subordination and superordination-preserving results of analytic functions involving the Liu-Owa integral operator. Sandwich-type result is also obtained.     

A unified presentation of some classes of meromorphically multivalent functions

The authors introduce and investigate various properties of a general class

U_k[p,a,β,A,B]

p, k ε N {1, 2, 3,…,}; 0 α < p; β 0

;

−1 A < B 1; 0 < B 1)

,which unifies and extends several (known or new) subclasses of meromorphically multivalent functions. The properties and characteristics of this general class, which are presented here, include growth and distortion theorems; they also involve Hadamard products (or convolution) of functions belonging to the class U_k[p,α,β,A,B].     

A class of functions synthesized from a finite number of examples and a lisp program scheme

We define a class of functions that can be synthesized from example problems. The algorithmic representation of these functions is the interpretation of a given scheme. The instantiation of the scheme variables is realized by a new method which uses pattern matching then if necessary generalization and further pattern matching. One can compute the number of examples necessary to characterize in a unique way a function of this class.