On neighborhood and partial sums problem for generalized Sakaguchi type functions

TL;DR

This paper introduces a new class of analytic functions with negative coefficients in the unit disk and investigates their coefficient estimates, neighborhoods, and partial sums.

Contribution

It defines a novel class of functions and provides new results on coefficient bounds, neighborhoods, and partial sums for these functions.

Findings

Derived coefficient estimates for the new class.

Established neighborhoods for functions in the class.

Analyzed partial sums and their properties.

Abstract

In the present investigation, we introduce a new class k-US_{s}^{{\eta}}({\lambda},{\mu},{\gamma},t) of analytic functions in the open unit disc U with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions f(z) belonging to this class.