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Article

Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator

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Department of Mechanical Engineering, Sarhad University of Science & Information Technology, Ring Road, Peshawar 25000, Pakistan
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Mathematics Section, Women’s College, Aligarh Muslim University, Aligarh 202001, Uttar Pradesh, India
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Department of Mathematics, Aligarh Muslim University, Aligarh 202001, Uttar Pradesh, India
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Department of Mathematics and Computer Science, Brandon University, 270 18th Street, Brandon, MB R7A 6A9, Canada
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Research Center for Interneural Computing, China Medical University, Taichung 40402, Taiwan, Republic of China
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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China
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Department of Mathematics, COMSATS University Islamabad, Wah Campus 47040, Pakistan
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(5), 719; https://doi.org/10.3390/sym11050719
Received: 18 April 2019 / Revised: 8 May 2019 / Accepted: 23 May 2019 / Published: 27 May 2019
(This article belongs to the Special Issue Integral Transformations, Operational Calculus and Their Applications)
This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed. View Full-Text
Keywords: Geometric Function Theory; q-integral operator; q-starlike functions of complex order; q-convex functions of complex order; (δ,q)-neighborhood Geometric Function Theory; q-integral operator; q-starlike functions of complex order; q-convex functions of complex order; (δ,q)-neighborhood
MDPI and ACS Style

Mahmood, S.; Raza, N.; AbuJarad, E.S.A.; Srivastava, G.; Srivastava, H.M.; Malik, S.N. Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator. Symmetry 2019, 11, 719. https://doi.org/10.3390/sym11050719

AMA Style

Mahmood S, Raza N, AbuJarad ESA, Srivastava G, Srivastava HM, Malik SN. Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator. Symmetry. 2019; 11(5):719. https://doi.org/10.3390/sym11050719

Chicago/Turabian Style

Mahmood, Shahid, Nusrat Raza, Eman S. A. AbuJarad, Gautam Srivastava, H. M. Srivastava, and Sarfraz Nawaz Malik. 2019. "Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator" Symmetry 11, no. 5: 719. https://doi.org/10.3390/sym11050719

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