On Certain Subclass of Analytic Functions

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p -valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.

Some subclasses of meromorphically multivalent functions associated with a linear operator

In this paper, new subclasses of analytic functions in the open unit disk which are defined using generalized integral operator are introduced. Several interesting properties of these classes are obtained, such as inclusion relationships and integral preserving properties are derived.

In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.

This paper examines two subclasses of multivalent analytic functions defined with higher-order derivatives. These classes of functions are generalizations of several known subclasses that have been studied in separate works. Moreover, we find several interesting results for functions in these classes, including subordination results, containment relations, and integral preserving properties.

In this paper, we investigate certain subclass of analytic functions on the open unit disc. This class generalizes the well-known class of [Formula: see text]-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

In the present investigation, subclasses of analytic functions with respect to symmetrical points which are defined by the generalized Bessel functions of the first kind of orderμare introduced. Furthermore, some alluring geometric properties of these classes, which include inclusion property, integral-preserving properties, coefficients, and distortion results are studied. Moreover, some consequences of our results are also given.

In the present paper, we obtain some inclusion relations and convolution properties for certain subclasses of analytic functions in the unit disk which are defined by the generalized Salagean operator. Relevant connections of the results presented here with those obtained in earlier works are pointed out.

In this paper, the author studies the fractional operator $$\mathbb {D}_\lambda ^{\nu , n}:\mathcal {A}\rightarrow \mathcal {A}$$ , for $$-\infty -1, n\in \mathbb {N}_0=\{0,1,2,\ldots \}$$ , introduced in a recent work. A class of analytic functions defined by this operator is introduced. Inclusion relations, convolution property, extreme points of the class and other results are given. Corollaries based on the results are also given.

In this paper we obtain sandwich type theorems, inclusion relationships, convolution properties and coefficient estimates of certain classes of p-valent analytic functions defined by a convolution. Several other new results are also obtained.

A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems

In this paper, we introduce and study certain subclasses of analytic and spiral-like functions of complex order involving the Srivastava–Attiya integral operator. We also investigate some inclusion relations along with integral preserving properties of these classes.

We introduce a class of univalent functions Rn(λ, α) defined by a new differential operator Dnf(z), n ∈ ℕ0 = {0, 1, 2, …}, where D0f(z) = f(z), D1f(z) = (1 − λ)f(z) + λzf′(z) = Dλf(z), λ ≥ 0, and Dnf(z) = Dλ(Dn−1f(z)). Inclusion relations, extreme points of Rn(λ, α), some convolution properties of functions belonging to Rn(λ, α), and other results are given.

Some subclasses of meromorphically multivalent functions associated with the generalized hypergeometric function

The paper aims to introduce a certain subclass S * g (A,B,,p,j) of the class * (p) of meromorphically multivalent functions with negative coefficients, defined by using the definitions of Hadamard product and subordination for two functions belong to the class * (p). We first investigate the geometric characterization property, giving the coefficient estimates for functions in the class S * g (A,B,,p,j). We also obtain the distortion theorem, radii of meromorphically p-valent starlikeness and convexity of order (0<p), neighborhood property, partial sums, convolution properties as well as integral operator and integral representation.