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http://dx.doi.org/10.5666/KMJ.2021.61.1.75

Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-calculus  

Ahuja, Om (Department of Mathematical Sciences, Kent State University)
Bohra, Nisha (Department of Mathematics, Sri Venkateswara College, University of Delhi)
Cetinkaya, Asena (Department of Mathematics and Computer Science, Istanbul Kultur University)
Kumar, Sushil (Bharati Vidyapeeth's college of Engineering)
Publication Information
Kyungpook Mathematical Journal / v.61, no.1, 2021 , pp. 75-98 More about this Journal
Abstract
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-Bieberbachde-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-$Szeg{\ddot{o}}$ inequalities; (p, q)-starlike functions; (p, q)-convex functions; (p, q)-logarithmic coefficient bounds; cardioid-shaped domain; q-Bieberbach-de-Branges type inequalities;
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