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Volume 7
Issue 4
10.3390/math7040316
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Article

On Geometric Properties of Normalized Hyper-Bessel Functions

by
Khurshid Ahmad
1,
Saima Mustafa
2,
Muhey U. Din
3,
Shafiq ur Rehman
4,
Mohsan Raza
5,* and
Muhammad Arif
1
1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
2
Department of Mathematics, PMAS Arid Agriculture University, Rawalpindi 46000, Pakistan
3
Department of Mathematics, Islamia College Faisalabad, Faisalabad 38000, Pakistan
4
Department of Mathematics, COMSATS University Islamabad, Attock 43600, Pakistan
5
Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 316; https://doi.org/10.3390/math7040316
Submission received: 18 February 2019 / Revised: 20 March 2019 / Accepted: 21 March 2019 / Published: 28 March 2019
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
Versions Notes

Abstract

In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc. We also study the Hardy spaces of hyper-Bessel functions.
Keywords: univalent functions; starlikeness; convexity; close-to-convexity; hyper-Bessel functions; Hardy space univalent functions; starlikeness; convexity; close-to-convexity; hyper-Bessel functions; Hardy space

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MDPI and ACS Style

Ahmad, K.; Mustafa, S.; Din, M.U.; ur Rehman, S.; Raza, M.; Arif, M. On Geometric Properties of Normalized Hyper-Bessel Functions. Mathematics 2019, 7, 316. https://doi.org/10.3390/math7040316

AMA Style

Ahmad K, Mustafa S, Din MU, ur Rehman S, Raza M, Arif M. On Geometric Properties of Normalized Hyper-Bessel Functions. Mathematics. 2019; 7(4):316. https://doi.org/10.3390/math7040316

Chicago/Turabian Style

Ahmad, Khurshid, Saima Mustafa, Muhey U. Din, Shafiq ur Rehman, Mohsan Raza, and Muhammad Arif. 2019. "On Geometric Properties of Normalized Hyper-Bessel Functions" Mathematics 7, no. 4: 316. https://doi.org/10.3390/math7040316

APA Style

Ahmad, K., Mustafa, S., Din, M. U., ur Rehman, S., Raza, M., & Arif, M. (2019). On Geometric Properties of Normalized Hyper-Bessel Functions. Mathematics, 7(4), 316. https://doi.org/10.3390/math7040316

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