期刊论文

英文

FILOMAT

0354-5180

2022

36

11

3845-3860

10.2298/FIL2211845L

2020 Mathematics Subject Classification. Primary 31A05; Secondary 30C45, 30C20 Keywords. Harmonic, univalent, slanted half-plane mappings, convex mappings, convex in a direction, and convolution. Received: 10 January 2021; Revised: 26 June 2022; Accepted: 18 August 2022 Communicated by Miodrag Mateljević The work of the first author is supported by NSF of Hunan (No. 2020JJ6038) and the Scientific Research Fund of Hunan Provincial Education Department (20A070), and partially supported by NSF of China (No. 12071116), the Science and Technology Plan Project of Hunan Province (No. 2016TP1020), and the Application-Oriented Characterized Disciplines, Double First-Class University Project of Hunan Province (Xiangjiaotong [2018]469). The work of the second author is supported in part by Mathematical Research Impact Centric Support (MATRICS) grant, File No.: MTR/2017/000367, by the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India. Email addresses: lanlimail2012@sina.cn (Liulan Li), samy@iitm.ac.in (Saminathan Ponnusamy)

本校为第一机构

In this paper, we mainly consider the convolutions of slanted half-plane mappings and strip mappings of the unit disk D. If f1 is a slanted half-plane mapping and f2 is a slanted half-plane mapping or a strip mapping, then we prove that f1 ∗ f2 is convex in some direction if f1 ∗ f2 is locally univalent in D. We also obtain two sufficient conditions for f1 ∗ f2 to be locally univalent in D. Our results extend many of the recent results in this direction. Moreover, we consider a class of harmonic mappings including slanted half-plane mappings...