A correct proof of logarithmic coefficients for Janowski type $(j,k)$-symmetric starlike functions

TL;DR

This paper corrects a previous proof regarding logarithmic coefficients of Janowski type $(j,k)$-symmetric starlike functions and introduces new related inequalities, enhancing the understanding of this function class.

Contribution

The paper provides a correct proof of a key theorem and presents new logarithmic coefficient inequalities for Janowski type $(j,k)$-symmetric starlike functions.

Findings

Corrected proof of Theorem 3 from previous work.

New logarithmic coefficient inequalities established.

Enhanced understanding of Janowski type $(j,k)$-symmetric starlike functions.

Abstract

Recently, authors [7] studied the logarithmic coefficient bounds for class of the Janowski type $(j,k)$-symmetric starlike functions $\mathcal{ST}_{[j,k]}(A,B)$ in ({\em Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.} (2022). DOI: 10.1007/s13398-022-01310-9). We pointed out that the proof of Theorem~3 in [7] is incorrect. In this article, we present the correct proof of Theorem~3. In addition, we also obtain some new results related to the logarithmic coefficient inequalities for the class $\mathcal{ST}_{[j,k]}(A,B)$.