On harmonic entire mappings

• Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 116; no. 1
• Main Authors: Deng, Hua, Ponnusamy, Saminathan, Qiao, Jinjing, Shan, Yanan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Original Paper; Theoretical; Upper bounds; Order; 30D20; Type; Close-to-convex and convex functions; Harmonic entire mapping; Univalent; Primary: 31A05; Secondary 30D10; Entire function; 31A05; 30D15
• ISSN: 1578-7303; 1579-1505
• DOI: 10.1007/s13398-021-01148-7

In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping f = h + g ¯ , respectively, and also consider the relationship between the order and the type of f , h , and g . Secondly, we investigate the harmonic mappings f = h + g ¯ such that f ( n p ) = h ( n p ) + g ( n p ) ¯ are univalent in the unit disk, where { n p } p = 1 ∞ be a strictly increasing sequence of nonnegative integers. In terms of the sequence { n p } p = 1 ∞ , we derive several necessary conditions for these mappings to be entire and also establish an upper bound for the order of these mappings.