Sentence examples for subclass of functions from inspiring English sources

Finally, denote by the subclass of functions in where.

We also prove that the results are sharp for a certain subclass of functions.

Let N1 denote the class of generalized Nevanlinna functions with one negative square and let N1, 0 be the subclass of functions Q z)∈N1 with the additional properties limy→∞ Q iy)/y=0 and lim supy→∞ y |Im Q iy)|<∞.

In the paper, we consider the classes of functions which generalize these subclasses of functions.

We give the precise asymptotic behavior of the Boolean radius of several natural subclasses of functions on finite Boolean cubes, as e.g. the class of all real functions on {−1,1}N, the subclass made of all homogeneous functions or certain threshold functions.

In this paper, we investigate the concept of first- and second-order approximations to generalize some results such as optimality conditions for a subclass of convex functions called strongly convex functions of order γ.

In 1929, the notion of exponential convexity was introduced by Bernstein [3]; later Widder [4] introduced these functions as a subclass of convex functions in a given interval ((a,b)).

It was found recently that natural gene regulatory systems are governed by hierarchically canalyzing functions (HCFs), a special subclass of Boolean functions.

The aim of this paper is to study the properties of a subclass of analytic functions related to p-valent Bazilevic functions by using the concept of differential subordination.

This subclass of tensor functions includes tensor power series, exponential tensor function, etc., and is more general than those investigated before.

The main object of the present paper is to introduce a subclass of analytic functions using the Dziok-Raina operator associated with the quasi hypergeometric functions.