Article
Kyungpook Mathematical Journal 2021; 61(1): 75-98
Published online March 31, 2021
Copyright © Kyungpook Mathematical Journal.
Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-calculus
Om Ahuja, Nisha Bohra, Asena Çetinkaya, Sushil Kumar*
Department of Mathematical Sciences, Kent State University, Ohio, 44021, U.S.A
e-mail : oahuja@kent.edu
Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi-110 021, India
email : nishib89@gmail.com
Department of Mathematics and Computer Science, İstanbul Kültür University, İstanbul, Turkey
e-mail : asnfigen@hotmail.com
Bharati Vidyapeeth's college of Engineering, Delhi-110063, India
e-mail : sushilkumar16n@gmail.com
Received: March 19, 2020; Revised: July 28, 2020; Accepted: July 28, 2020
In this paper, we introduce new classes of post-quantum or (p,q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p,q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p,q)-logarithmic coefficients. In addition, we get q-Bieberbach-de-Branges type inequalities for the special case of our classes when p=1. Moreover, we also discuss some special cases of the obtained results.
Keywords: (p, q)-Fekete-Szegö, inequalities, (p,q)-starlike functions, (p,q)-convex functions, (p,q)-logarithmic coefficient bounds, cardioid-shaped domain, q-Bie