Univalence of Logharmonic Integrals of Cesàro Type Operator

Abstract

This manuscript extends the integral transform (Formula presented.) where φ is normalized analytic function, to the case of logharmonic mapping and study their univalence properties. This integral transform carries the well-known Alexander (i.e. C01) and Cesáro (i.e. C11) transforms. Following the idea of classical shear construction for harmonic mappings, we employ the shear construction for logharmonic mappings that is introduced by Liu and Ponnusamy in 2022 with a goal to generate logharmonic integrals of Cesáro type. In addition, intriguing relationships between harmonic and non-vanishing logharmonic integrals corresponding to the integral transforms Cβα are established. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2024.