On $\lambda-$ Pseudo bi-starlike functions related with Fibonacci numbers

TL;DR

This paper introduces a new subclass of bi-pseudo-starlike functions connected with Fibonacci numbers, analyzes their coefficients, and establishes Fekete-Szeg"o inequalities, providing new insights into Fibonacci-related geometric function theory.

Contribution

It defines a novel class of $ ext{lambda}$-bi-pseudo-starlike functions linked with Fibonacci numbers and derives coefficient bounds and Fekete-Szeg"o results for this class.

Findings

Determined initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for the new class.

Established Fekete-Szeg"o inequalities for the class.

Presented new corollaries, some of which are original contributions.

Abstract

In this paper we define a new subclass $\lambda$-bi-pseudo-starlike functions of $\Sigma$ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for $f\in\mathcal{PSL}_{\Sigma}^\lambda(\tilde{p}(z)).$ Further we determine the Fekete-Szeg\"{o} result for the function class $\mathcal{PSL}_{\Sigma}^\lambda(\tilde{p}(z))$ and for special cases, corollaries are stated which some of them are new and have not been studied so far.