Functional inequalities for several classes of <i>q</i>-starlike and <i>q</i>-convex type analytic and multivalent functions using a generalized Bernardi integral operator

Pinhong Long; Huo Tang; Wenshuai Wang; Pinhong Long; Huo Tang; Wenshuai Wang

doi:10.3934/math.2021073

AIMS Mathematics

2021, Volume 6, Issue 2: 1191-1208. doi: 10.3934/math.2021073

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Research article

Functional inequalities for several classes of q-starlike and q-convex type analytic and multivalent functions using a generalized Bernardi integral operator

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningixa 750021, People's Republic of China
2.
School of Mathematics and Computer Sciences, Chifeng University, Chifeng, Inner Mongolia, 024000, People's Republic of China

Received: 22 August 2020 Accepted: 26 October 2020 Published: 12 November 2020
MSC : 26A33, 30C45, 30C50

In the article we introduce and investigate several new subclasses of q-starlike and q-convex type analytic and multivalent functions involving a generalized Bernardi integral operator, and establish the Fekete-Szegö type functional inequalities for these function classes. Besides, the corresponding bound estimates of the coefficients a_p+1 and a_p+2 are obtained.
- Fekete-Szegö problem,
- analytic function,
- multivalent function,
- q-derivative operator,
- Bernardi integral operator
Citation: Pinhong Long, Huo Tang, Wenshuai Wang. Functional inequalities for several classes of q-starlike and q-convex type analytic and multivalent functions using a generalized Bernardi integral operator[J]. AIMS Mathematics, 2021, 6(2): 1191-1208. doi: 10.3934/math.2021073

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Abstract

In the article we introduce and investigate several new subclasses of q-starlike and q-convex type analytic and multivalent functions involving a generalized Bernardi integral operator, and establish the Fekete-Szegö type functional inequalities for these function classes. Besides, the corresponding bound estimates of the coefficients a_p+1 and a_p+2 are obtained.

References

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