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Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator

Year 2023, Volume: 72 Issue: 4, 1201 - 1210, 29.12.2023

Tuğba Yavuz Şahsene Altınkaya

https://doi.org/10.31801/cfsuasmas.1300217

Abstract

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.

Keywords

Spirallike function coefficient estimate subordination q-integral operator.

References

  • 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.
  • 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
  • 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
  • Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), 429–446.
  • 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
  • Gasper, G., Rahman, M., Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  • 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
  • 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
  • Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 14 (1910), 193-203.
  • Libera, R. J., Univalent $\alpha$-spiral functions, Canadian Journal of Mathematics, 19 (1967), 449–456.
  • 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.
  • 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.
  • Noor, K. I., Riaz, S., Noor, M. A., On q-Bernardi integral operator, TWMS J. Pure Appl. Math., 8 (1) (2017), 3–11.
  • Purohit, S. D., Raina, R. K., Certain subclasses of analytic functions associated with fractional q-calculus operators, Mathematica Scandinavica, (2011), 55-70.
  • 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
  • Shareef, Z., Hussain, S., Darus, M., Convolution operators in the geometric function theory, J. Inequal. Appl., 2012 (2012), 213.
  • Spacek, L., Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62 (1933), 12–19.
  • 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.
  • 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
  • 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.
  • 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.

Year 2023, Volume: 72 Issue: 4, 1201 - 1210, 29.12.2023

Tuğba Yavuz Şahsene Altınkaya

https://doi.org/10.31801/cfsuasmas.1300217

Abstract

References

  • 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.
  • 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
  • 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
  • Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), 429–446.
  • 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
  • Gasper, G., Rahman, M., Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  • 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
  • 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
  • Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 14 (1910), 193-203.
  • Libera, R. J., Univalent $\alpha$-spiral functions, Canadian Journal of Mathematics, 19 (1967), 449–456.
  • 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.
  • 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.
  • Noor, K. I., Riaz, S., Noor, M. A., On q-Bernardi integral operator, TWMS J. Pure Appl. Math., 8 (1) (2017), 3–11.
  • Purohit, S. D., Raina, R. K., Certain subclasses of analytic functions associated with fractional q-calculus operators, Mathematica Scandinavica, (2011), 55-70.
  • 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
  • Shareef, Z., Hussain, S., Darus, M., Convolution operators in the geometric function theory, J. Inequal. Appl., 2012 (2012), 213.
  • Spacek, L., Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62 (1933), 12–19.
  • 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.
  • 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
  • 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.
  • 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.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Tuğba Yavuz 0000-0002-0490-9313

Şahsene Altınkaya 0000-0002-7950-8450

Publication Date December 29, 2023
Submission Date May 21, 2023
Acceptance Date June 7, 2023
Published in Issue Year 2023 Volume: 72 Issue: 4

Cite

APA Yavuz, T., & Altınkaya, Ş. (2023). Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(4), 1201-1210. https://doi.org/10.31801/cfsuasmas.1300217
AMA Yavuz T, Altınkaya Ş. Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2023;72(4):1201-1210. doi:10.31801/cfsuasmas.1300217
Chicago Yavuz, Tuğba, and Şahsene Altınkaya. “Sharp Coefficient Estimates for $\vartheta$-Spirallike Functions Involving Generalized Q-Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 4 (December 2023): 1201-10. https://doi.org/10.31801/cfsuasmas.1300217.
EndNote Yavuz T, Altınkaya Ş (December 1, 2023) Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 4 1201–1210.
IEEE T. Yavuz and Ş. Altınkaya, “Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 4, pp. 1201–1210, 2023, doi: 10.31801/cfsuasmas.1300217.
ISNAD Yavuz, Tuğba - Altınkaya, Şahsene. “Sharp Coefficient Estimates for $\vartheta$-Spirallike Functions Involving Generalized Q-Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/4 (December 2023), 1201-1210. https://doi.org/10.31801/cfsuasmas.1300217.
JAMA Yavuz T, Altınkaya Ş. Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:1201–1210.
MLA Yavuz, Tuğba and Şahsene Altınkaya. “Sharp Coefficient Estimates for $\vartheta$-Spirallike Functions Involving Generalized Q-Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 4, 2023, pp. 1201-10, doi:10.31801/cfsuasmas.1300217.
Vancouver Yavuz T, Altınkaya Ş. Sharp coefficient estimates for $\vartheta$-spirallike functions involving generalized q-integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(4):1201-10.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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