Application of q-Mittag-Leffer Function on Certain Subclasses of Analytic Functions

The main objective of this paper is to introduce and investigate various properties and characteristics of a unified class of analytic functions with negative coefficient in the unit disc. The results presented here involve distortion inequalities and growth and distortion theorem involving fractional integrals and fractional derivatives. Keywords: Analytic functions; Univalent functions; Riemann - Liouville operators ; Growth and distortion theorem; Fractional derivatives.

The aim of this article is to introduce and study certain subclasses of analytic functions and we investigate various properties of these classes such as inclusion properties and convex convolution preserving properties. Also, some related applications are discussed.

The radius of starlikeness of certain subclasses of analytic functions

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 this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order r.

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.

Neighborhoods of certain subclasses of analytic functions of complex order with negative coefficients

The object of the present investigation is to solve the Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a new class R(a,c) of analytic functions involving the Carlson-Shaffer operator in the unit disk. We also obtain a sufficient condition for normalized analytic functions in the unit disk to be in this class.

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.

In the present paper, we have introduced a new subclass of analytic functions involving integral operator defined by polylogarithm function. Necessary and sufficient conditions are obtained for this class. Further distortion theorem, linear combination and results on partial sums are investigated.

In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator Dr. We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which Drl′(z)ϑzDrl′(z)Drl(z)1−ϑ≺ez (0≤ϑ≤1) lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained.

In this work, we introduce certain subclasses of analytic functions involving the integral operators that generalize the class of uniformly starlike, convex, and close-to-convex functions with respect to symmetric points. We then establish various inclusion relations for these newly defined classes.

This study of Hankel and Hermitian Toeplitz determinants is one of the major areas of interest in Geometric function theory and has wide applications in the areas of signal processing and Applied Mathematics. In our present investigations, we define a new subclass of normalized analytic functions H(λ)(λ≥0), defined using a subordination relation with the sine function K(z)=1+sinz. For the class H(λ), coefficient estimates, upper and lower bounds for the Hermitian Toeplitz determinants of second and third order are found. In addition, estimates are provided for the second and third-order Hankel determinants for the class H(λ).

Gegenbauer polynomials constitute a numerical tool that has attracted the interest of many function theorists in recent times mainly due to their real-life applications in many areas of the sciences and engineering. Their applications in geometric function theory (GFT) have also been considered by many researchers. In this paper, this powerful tool is associated with the prolific concepts of convolution and subordination. The main purpose of the research contained in this paper is to introduce and study a new subclass of analytic functions. This subclass is presented using an operator defined as the convolution of the generalized distribution and the error function and applying the principle of subordination. Investigations into this subclass are considered in connection to Carathéodory functions, the modified sigmoid function and Bell numbers to obtain coefficient estimates for the contained 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.