ON A CERTAIN CLASS OF ANALYTIC UNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS DEFINED BY q-CALCULUS 

By

S. N. Mishra1, I. B. Mishra2 and S. Porwal3

1Department of Mathematics, Brahmanand Postgraduate College The Mall, Kanpur-208001, Uttar Pradesh, India 

2Department of Mathematics, Janta College, Bakewar, Etawah-206124, Uttar Pradesh, India 

3Department of Mathematics, Ram Sahai Government Degree College, Bairi-Shivrajpur, Kanpur-209205, Uttar Pradesh, India Email:snmishra2006@gmail.com, dr.indubalamishra@yahoo.com, saurabhjcb@rediffmail.com 

(Received : January 18, 2021; In format : June 22, 2021, Accepted: May 26, 2022) 

 DOI: https://doi.org/10.58250/Jnanabha.2022.52127

Abstract

The main object of this paper is to introduce a new subclass of analytic univalent functions by using q-calculus. We obtain results regarding coefficient estimates extreme points, distortion bounds, convolution condition and convex combination for this class. Finally, we discuss a class preserving integral operator for this class. Relevant connections of the results presented herewith various well-known results are briefly indicated. 

2020 Mathematical Sciences Classification: 30C45. 

Keywords and Phrases: Analytic, univalent, Salagean operator, q-calculus