Some properties of a class of analytic functions involving a new generalized differential operator

Abstract

In the present paper, we introduce a new generalized differentialoperator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the openunit disc $U=\left\{ z\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closuretheorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained

A New Class of Function with Finitely Many Fixed Points

“…Perhaps, this is the reason why the study of differential operators is growing interest in Geometric Functions Theory and Application (GFTA). Some of the numerous differential operators (multiplier transformations) established by some authors are found in [5][6][7][8][9][10][11].…”

On a Harmonic Univalent Subclass of Functions Involving a Generalized Linear Operator

“…where I m δ,µ,λ,η,ς,τ f (z) is defined by (4). For relevant and recent references related to this work, we refer the reader to [13][14][15][16][17][18][19][20].…”

Initial bounds for analytic and bi-univalent functions by means of (p,q)−Chebyshev polynomials defined by differential operator

“…It's still an open problem. Since then, there have been many researchers (see [2,5,6,7,11,12,14,15,13]) investigated several interesting subclasses of the class Σ and found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |. In fact, its worth to mention that by making use of the Faber polynomial coefficient expansions Jahangiri, Jay M., and Samaneh G. Hamidi [8] have obtained estimates for the general coefficients |a n | for bi-univalent functions subject to certain gap series.…”