TY  - JOUR
T1  - Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator
AU  - Yavuz, Tuğba
AU  - Altınkaya, Şahsene
PY  - 2023
DA  - December
Y2  - 2023
DO  - 10.31801/cfsuasmas.1300217
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 1201
EP  - 1210
VL  - 72
IS  - 4
LA  - en
AB  - The aim of this article is to identify a new subfamily of spirallike functions and then to demonstrate necessary and sufficient conditions, sharp coefficients estimates for functions in this subfamily.
KW  - Spirallike function
KW  - coefficient estimate
KW  - subordination
KW  - q-integral operator.
CR  - Ahuja, O. P., Çetinkaya, A., Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095 (1) (2019), 1-14.
CR  - Altınkaya, Ş., On the inclusion properties for $\vartheta$-spirallike functions involving both Mittag-Leffler and Wright function, Turkish J. Math., 46 (3) (2022), 1119-1131. https://doi.org/10.55730/1300-0098.3147
CR  - Aouf, M. K., Seoudy, T. M., Convolution properties for classes of bounded analytic functions with complex order defined by q-derivative operator, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 113 (2) (2019), 1279-1288. https://doi.org/10.1007/s13398-018-0545-5
CR  - Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), 429–446.
CR  - Bulut, S., Certain subclasses of analytic and bi-univalent functions involving the q-derivative operator, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 66 (1) (2017), 108-114.
https://doi.org/10.1501/Commua1-0000000780
CR  - Gasper, G., Rahman, M., Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
CR  - Govindaraj, M., Sivasubramanian, S., On a class of analytic functions related to conic domains involving q-calculus, Anal. Math., 43 (3) (2017), 475-487. https://doi.org/10.1007/s10476-017-0206-5
CR  - Jackson, F.H., On q-functions and a certain difference operator, Earth and Environmental Science Transactions of the Royal Society of Edinburgh, 46 (1908), 253–281. https://doi.org/10.1017/S0080456800002751
CR  - Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 14 (1910), 193-203.
CR  - Libera, R. J., Univalent $\alpha$-spiral functions, Canadian Journal of Mathematics, 19 (1967), 449–456.
CR  - 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 q-integral operators, Symmetry, 11 (2019), 719.
CR  - Mustafa, N., Korkmaz, S., The sharp inequality for the coefficients of certain subclass of analytic functions defined by q-derivative, Journal of Scientific and Engineering Research, 7 (4) (2020), 209-218.
CR  - Noor, K. I., Riaz, S., Noor, M. A., On q-Bernardi integral operator, TWMS J. Pure Appl. Math., 8 (1) (2017), 3–11.
CR  - Purohit, S. D., Raina, R. K., Certain subclasses of analytic functions associated with fractional q-calculus operators, Mathematica Scandinavica, (2011), 55-70.
CR  - Raza, M, Srivastava, H. M., Arif, M., Ahmad, K., Coefficient estimates for a certain family of analytic functions involving a q-derivative operator, Ramanujan J., 55 (1) (2021), 53-71.
https://doi.org/10.1007/s11139-020-00338-y
CR  - Shareef, Z., Hussain, S., Darus, M., Convolution operators in the geometric function theory, J. Inequal. Appl., 2012 (2012), 213.
CR  - Spacek, L., Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62 (1933), 12–19.
CR  - Srivastava, H. M., Univalent functions, fractional calculus, and associated generalized hypergeometric functions, in Univalent Functions, Fractional Calculus, and Their Applications (H. M. Srivastava and S. Owa, Editors), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
CR  - Srivastava, H. M., Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran J Sci Technol Trans Sci., 44 (1) (2020), 327-344. https://doi.org/10.1007/s40995-019-00815-0
CR  - Xu, Q. H., Cai, Q. M., Srivastava, H. M., Sharp coefficient estimates for certain subclasses of starlike functions of complex order, Appl. Mathe. Comput., 225 (2013), 43-49.
CR  - Yavuz, T., Coefficient estimates for certain subclass for spirallike functions defined by means of generalized Attiya-Srivastava operator, Commun. Korean Math. Soc., 31 (4) (2016), 703-712.
UR  - https://doi.org/10.31801/cfsuasmas.1300217
L1  - https://dergipark.org.tr/en/download/article-file/3156044
ER  -