Volume 10 (2018), Number 1

Some Properties of Certain Subclasses of Analytic Functions Associated with Generalized Differential Operator Involving Mittag-Leffler Function

Author(s): SUHILA ELHADDAD and MASLINA DARUS

Abstract: A subclass in the open unit disc of analytic functions is introduced in this paper. This subclass ${\mathcal{𝒮}}_{𝜗}^{m,\delta }\left(\lambda ,\alpha ,\beta ,A,B\right)$ is mainly defined by generalized differential Operator. Some interesting properties of this class are also obtained.

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On Weighted Ostrowski Grüss Inequality with Applications

Author(s): NAZIA IRSHAD and ASIF R. KHAN

Abstract: The purpose of present article is to obtain weighted Ostrowski Grüss type inequality for differentiable functions by using weighted Korkine’s identity. We also discussed its applications into probability density function and numerical quadrature rules.

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Second and Third Hankel Determinant for a Class Defined by Generalized Polylogarithm Functions

Author(s): MOHD NAZRAN MOHAMMED PAUZI, MASLINA DARUS and SAIBAH SIREGAR

Abstract: By making use of ${𝔇}_{\lambda }^{m}f\left(z\right)$, the generalized Polylogarithms derivative operator introduced by Al-Saqsi and Darus [4] defined by

$${𝔇}_{\lambda }^{m}f\left(z\right)=z+\sum _{n=2}^{\infty }\frac{n^m\left(n+\lambda -1\right)!}{\lambda !\left(n-1\right)!}{a}_n{z}^n,$$

where $m\in {\mathbb{N}}_0=\left\{0,1,2,3,...\right\}$. The sharp upper bound for the second Hankel determinant $H_{2,2}\left(f\right)$ and third Hankel determinant $H_{3,1}\left(f\right)$ is obtained. Relevant connections of the results presented here with those given in earlier works are also indicated.

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