Close-to-Convexity of Convolutions of Classes of Harmonic Functions. (2nd May 2018)

• Record Type: Journal Article
• Authors: Garg, Raj Kumar; Jahangiri, Jay M.
• Other Names: Bulboaca Teodor Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2018(2018)
• Publication Date: 2018-05-02
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2018/3808513
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Forj = 1, 2 and for positive integersm andn, we consider classes of harmonic functionsf j = h j + g j ¯, whereg 1 ( z ) = z n h 1 ( z ) andg 2 ′ ( z ) = z n h 2 ′ ( z ) org 1 ′ ( z ) = z n h 1 ′ ( z ) andg 2 ′ ( z ) = z m h 2 ′ ( z ), and we prove that their convolutionf 1 ⁎ f 2 = h 1 ⁎ h 2 + g 1 ⁎ g 2 ¯ is locally one-to-one, sense-preserving, and close-to-convex harmonic inz < 1 .