Horadam polynomials for a new family of λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}-pseu

In the present article, we introduce and study a new family $$\mathcal {F}_{\Sigma }(\delta ,\lambda ,m,n,r)$$ of normalized analytic and bi-univalent functions associating $$\lambda $$ -pseudo functions with Sakaguchi type functions by using the Horadam polynomials. We obtain upper bounds for the initial Taylor–Maclaurin coefficients $$|a_2|$$ and $$|a_3|$$ . Further we obtain the Fekete–Szego inequality for functions in the family $$\mathcal {F}_{\Sigma }(\delta ,\lambda ,m,n,r)$$ which we have introduced here. We also indicate several certain special cases and consequences for our results.