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## Partial sums of hyper-Bessel function with applications

#### İbrahim AKTAŞ [1]

The main purpose of the presented paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its partial sum. In addition, some applications related to the obtained results are given.
Analytic function, univalent function, partial sum, trigonometric function, hyper Bessel function
• [1] İ. Aktaş and H. Orhan, Distortion bounds for a new subclass of analytic functions and their partial sums, Bull. Transilv. Univ. Braşov Ser. III, 57 (2), 1–12, 2015.
• [2] İ. Aktaş and H. Orhan, Partial sums of Normalized Dini Functions, J. Classical Anal. 9 (2), 127–135, 2016.
• [3] İ. Aktaş and H. Orhan, On Partial sums of Normalized q-Bessel Functions, Commun. Korean Math. Soc. 33 (2), 535–547, 2018.
• [4] D. Bansal and H. Orhan, Partial sums of Mittag-Leffler function, J. Math. Inequal. 12 (2), 423–431, 2018.
• [5] H. Chaggara and N.B. Romdhane, On the zeros of the hyper-Bessel function, Integral Transforms Spec. Funct. 26 (2), 96–101, 2015.
• [6] M. Çağlar and E. Deniz, Partial sums of the normalized Lommel functions, Math. Inequal. Appl. 18 (3), 1189–1199, 2015.
• [7] B.A. Frasin, Generalization of partial sums of certain analytic and univalent functions, Appl. Math. Lett. 21, 735-741, 2008.
• [8] A.W. Goodman, Univalent functions, vol. 1, Mariner Publishing Company, Inc., 1983.
• [9] H. Orhan and N. Yağmur, Partial sums of Generilazed Bessel Functions, J. Math. Inequal. 8 (4), 863–877, 2014.
• [10] S. Owa, H.M. Srivastava and N. Saito, Partial sums of certain classes of analytic functions, Int. J. Comput. Math. 81 (10), 1239–1256, 2004.
• [11] D. Răducanu, On partial sums of normalized Mittag-Leffler functions, An. Şt. Univ. Ovidius Constanta, 25 (2), 123–133, 2017.
• [12] T. Sheil-Small, A note on partial sums of convex schlicht functions, Bull. London Math. Soc. 2, 165–168, 1970.
• [13] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209, 221–227, 1997.
• [14] E.M. Silvia, On partial sums of convex functions of order α. Houston J. Math. 11, 397–404, 1985.
• [15] G.N. Watson, A Tretaise on the Theory of Bessel Functions. Second edition, London and New York, Cambridge University Press, 1944.
• [16] N. Yağmur and H. Orhan, Partial sums of Generilazed Struve Functions, Miskolc Math. Notes, 17 (1), 657-670, 2016.
Primary Language en Mathematics Mathematics Orcid: 0000-0003-4570-4485Author: İbrahim AKTAŞ (Primary Author)Institution: KARAMANOGLU MEHMETBEY UNIVERSITYCountry: Turkey Publication Date : February 6, 2020
 Bibtex @research article { hujms470930, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {380 - 388}, doi = {10.15672/hujms.470930}, title = {Partial sums of hyper-Bessel function with applications}, key = {cite}, author = {AKTAŞ, İbrahim} } APA AKTAŞ, İ . (2020). Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 380-388 . DOI: 10.15672/hujms.470930 MLA AKTAŞ, İ . "Partial sums of hyper-Bessel function with applications". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 380-388 Chicago AKTAŞ, İ . "Partial sums of hyper-Bessel function with applications". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 380-388 RIS TY - JOUR T1 - Partial sums of hyper-Bessel function with applications AU - İbrahim AKTAŞ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.470930 DO - 10.15672/hujms.470930 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 380 EP - 388 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.470930 UR - https://doi.org/10.15672/hujms.470930 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Partial sums of hyper-Bessel function with applications %A İbrahim AKTAŞ %T Partial sums of hyper-Bessel function with applications %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.470930 %U 10.15672/hujms.470930 ISNAD AKTAŞ, İbrahim . "Partial sums of hyper-Bessel function with applications". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 380-388 . https://doi.org/10.15672/hujms.470930 AMA AKTAŞ İ . Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 380-388. Vancouver AKTAŞ İ . Partial sums of hyper-Bessel function with applications. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 388-380.

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