Certain Classes of Analytic Functions Related to the Crescent-Shaped Regions

R. K. Raina; P. Sharma; J. Sokół

doi:10.3103/S1068362318060067

Certain Classes of Analytic Functions Related to the Crescent-Shaped Regions

Authors: Raina R.K.¹, Sharma P.², Sokół J.³
Affiliations:
1. University of Agriculture and Technology
2. University of Lucknow
3. University of Rzeszów
Issue: Vol 53, No 6 (2018)
Pages: 355-362
Section: Real and Complex Analysis
URL: https://journal-vniispk.ru/1068-3623/article/view/228262
DOI: https://doi.org/10.3103/S1068362318060067
ID: 228262

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Abstract

In this paper, we study certain classes of analytic functions which satisfy a subordination condition and are associated with the crescent-shaped regions. We first give certain integral representations for the functions belonging to these classes and also present a relevant example. Making use of some known lemmas, we derive sufficient conditions for the functions to be in these classes. Some results on coefficient estimates are also obtained.