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

Sushil Kumar|Asena Cetinkaya|Om Ahuja|Nisha Bohra
경북대학교 자연과학대학 수학과|2021.03|Kyungpook Mathematical Journal|제61권 제1호|pp. 75-98

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키워드

(pq)-Fekete-Szeg¨o inequalitiesq)-starlike functionsq)- convex functionsq) logarithmic coefficient boundscardioid-shaped domainqBieberbach-de-Branges type inequalities.
주제분류수학

초록

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-Szeg¨o 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.

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-Szeg¨o 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.

참고문헌 (30)

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