A study of a new subclass of analytic functions with negative coefficients
Applicable Nonlinear Analysis, Volume 2, Issue 3, December 2025, Pages: 167–181
MUHAMMET KAMALI
Kyrgyz-Turkish Manas University, Faculty of Sciences, Department of Mathematics, Chyngz Aitmatov Avenue, Bishkek, Kyrgyz Republic
KILIÇBEK MARKAEV
Kyrgyz-Turkish Manas University, Faculty of Sciences, Department of Mathematics, Chyngz Aitmatov Avenue, Bishkek, Kyrgyz Republic
Abstract
In this paper,we introduce the subclasses \(A_{j}(n,m,\lambda ,\alpha )\) and \(T_{j}(n,m,\lambda ,\alpha )\) defined by generalized Salagean operator \(D_{\lambda }^{n}\). Coefficients estimates for the function belong to class \(T_{j}(n,m,\lambda ,\alpha )\) and distortion theorems are given. By making use of the familiar concept of neighborhoods of analytic functions is defined the neighborhoods of functions in the class \(T_{j}(n,m,\lambda,\alpha )\). Furthermore, distortion theorems for fractional calculius of functions in the class \(T_{j}(n,m,\lambda ,\alpha )\) has been studied. Additionally, Upper bound of the Hankel determinants \(H_{2,1}(f)\) for the coefficients of the functions belonging to class \(A(n,m,\lambda ,\alpha )\) determined.
Cite this Article as
Muhammet Kamali and Kiliçbek Markaev, A study of a new subclass of analytic functions with negative coefficients, Applicable Nonlinear Analysis, 2(3), 167–181, 2025