Inclusion Properties Of Certain Subclasses Research Articles

An Application of Poisson Distribution Series on Harmonic Classes of Analytic Functions

Many authors have obtained some inclusion properties of certain subclasses of univalent and functions associated with distribution series, such as Pascal distribution, Binomial distribution, Poisson distribution, Mittag–Leffler-type Poisson distribution, and Geometric distribution. In the present paper, we obtain some inclusion relations of the harmonic class H(α,δ) with the classes SH* of starlike harmonic functions and KH of convex harmonic functions, also for the harmonic classes TNHβ and TRHβ associated with the operator Υ defined by applying certain convolution operator regarding Poisson distribution series. Several consequences and corollaries of the main results are also obtained.

Some Inclusion Properties of Certain Subclasses of Analytic Functions Defined by Using the Tremblay Fractional Derivative Operator

In this paper, we introduce new subclasses of analytic and p-valent functions related to starlike, convex, close-to-convex, and quasi-convex functions by using a p-valent analog of the Tremblay fractional derivative operator. Inclusion relationships for these subclasses are established.

Inclusion properties for certain subclasses of analytic functions defined by using the generalized Bessel functions

By making use of the operator $B_\nu^c$ defined by the generalized Bessel functions of the first kind, the authors introduce and investigate several new subclasses of starlike, convex, close-to-convex and quasi-convex functions. The authors establish inclusion relationships associated with the aforementioned operator. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

Inclusion properties for certain subclasses of p-valent functions associated with new generalized derivative operator

In this paper we introduce several new classes of p-valent functions defined by new generalized derivative operator and investigate various inclusion properties of these classes. Some interesting applications involving classes of integral operators are also considered.

Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator

Let \(A\) denote the class of analytic functions with the normalization \(f(0)=f^{\prime }(0)-1=0\) in the open unit disc \(U=\{z:\left\vert z\right\vert <1\}\). Set \[f_{\lambda }^{n}(z)=z+\sum_{k=2}^{\infty }[1+\lambda (k-1)]^{n}z^{k}\quad(n\in N_{0};\ \lambda \geq 0;\ z\in U),\] and define \(f_{\lambda ,\mu }^{n}\) in terms of the Hadamard product \[f_{\lambda }^{n}(z)\ast f_{\lambda ,\mu }^{n}=\frac{z}{(1-z)^{\mu }}\quad (\mu >0;\ z\in U). \] In this paper, we introduce several subclasses of analytic functions defined by means of the operator \(I_{\lambda ,\mu }^{n}:A\longrightarrow A\), given by \[ I_{\lambda ,\mu }^{n}f(z)=f_{\lambda ,\mu }^{n}(z)\ast f(z)\quad (f\in A;\ n\in N_{0;}\ \lambda \geq 0;\ \mu >0). \]Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Inclusion Properties for Certain Subclasses of Analytic Functions Defined by a Linear Operator

The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered.

Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators

A known family of fractional integral operators (with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk 𝕌. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

Inclusion Properties for Certain Subclasses of Analytic Functions Associated with the Dziok-Srivastava Operator

The purpose of the present paper is to introduce several new classes of analytic functions defined by using the Choi-Saigo-Srivastava operator associated with the Dziok-Srivastava operator and to investigate various inclusion properties of these classes. Some interesting applications involving classes of integral operators are also considered.

Inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation

Let A denote the class of analytic functions with the normalization ƒ (0) = ƒ′(0)-1 = 0 in the open unit disk U, set f λ s ( z ) = z + ∑ k = 2 ∞ ( k + λ 1 + λ ) s z k ( s ∈ ℝ ; λ > - 1 ; z ∈ U ) and define ƒ λ,μ s , in terms of the Hadamard product f λ s ( z ) ∗ f λ , μ s ( z ) = z ( 1 − z ) μ ( μ > 0 ; z ∈ U ) In this paper, the authors introduce several new subclasses of analytic functions defined by means of the operator I λ,μ s : A → A, given by I λ , μ s f ( z ) = f λ , μ s ( z ) ∗ f ( z ) ( f ∈ A ; s ∈ ℝ ; λ > - 1 ; μ > 0 ) Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.

Some classes of analytic functions involving Noor integral operator

The object of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions defined by using the Noor integral operator. The integral preserving properties in connection with the operator are also considered. Relevant connections of the results presented here with those obtained in earlier works are pointed out.