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Notes on some classes of spirallike functions associated with the $q$-integral operator

Year 2024, Volume: 53 Issue: 1, 53 - 61, 29.02.2024

Tuğba Yavuz Şahsene Altınkaya

https://doi.org/10.15672/hujms.1180981

Abstract

The object of the present paper is to find the essential properties for certain subfamilies of analytic and spirallike functions which are generated by $q$-integral operator. Further, we derive membership relations for functions belong to these subfamilies, and also we determine coefficient estimates.

Keywords

Spirallike function convolution $q$-integral operator

References

  • [1] O. Ahuja and A. Çetinkaya, Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095 (1), 1-14, 2019.
  • [2] O. Ahuja, A. Çetinkaya and N. K. Jain, Analytic functions with conic domains associated with certain generalized $q$-integral operator, arXiv preprint arXiv:2012.13776.
  • [3] S. Altınkaya, On the inclusion properties for $\vartheta $-spirallike functions involving both Mittag-Leffler and Wright function, Turkish J. Math. 46 (3), 1119-1131, 2022.
  • [4] M. K. Aouf and T. M. Seoudy, Convolution properties for classes of bounded analytic functions with complex order defined by $q$-derivative operator, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113 (2), 1279-1288, 2019.
  • [5] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135, 429–446, 1969.
  • [6] S. Bulut, Certain subclasses of analytic and bi-univalent functions involving the $q$-derivative operator, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 66 (1), 108- 114, 2017.
  • [7] G. Gasper and M. Rahman, Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  • [8] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving $q$-calculus,Anal. Math. 43 (3), 475-487, 2017.
  • [9] F. H. Jackson, On $q$-functions and a certain difference operator, Earth Environ. Sci. Trans. R. Soc. Edinb. 46, 253–281, 1908.
  • [10] F. H. Jackson, On $q$-definite integrals, Q. J. Pure Appl. Math. 14, 193-203, 1910.
  • [11] S. Mahmood, N. Raza, E. S. A. Abujarad, G. Srivastava, H. M. Srivastava, S. N. Malik, Geometric properties of certain classes of analytic functions associated with $q$-integral operators, Symmetry, 11 (5), 1-14, 2019.
  • [12] N. Mustafa and S. Korkmaz, The sharp inequality for the coefficients of certain subclass of analytic functions defined by $q$-derivative, Journal of Scientific and Engineering Research 7 (4), 209-218, 2020.
  • [13] K. I. Noor, S. Riaz and M. A. Noor, On $q$-Bernardi integral operator, TWMS J. Pure Appl. Math. 8 (1), 3–11, 2017.
  • [14] S. D. Purohit and R. K. Raina, Certain subclasses of analytic functions associated with fractional $q$-calculus operators, Math. Scand. 109 (1), 55-70, 2011.
  • [15] M. Raza, H. M. Srivastava, M. Arif and K. Ahmad, Coefficient estimates for a certain family of analytic functions involving a $q$-derivative operator, Ramanujan J. 55 (1), 53-71, 2022.
  • [16] Z. Shareef, S. Hussain and M. Darus, Convolution operators in the geometric function theory, J. Inequal. Appl. 2012 (213), 1-11, 2012.
  • [17] H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 1, 48-61, 1985.
  • [18] L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62, 12–19, 1933.
  • [19] H. M. Srivastava, 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.
  • [20] H. M. Srivastava, 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. A Sci. 44 (1), 327-344, 2020.
  • [21] Q. H. Xu, C. B. Lv, N. C. Luo and H. M. Srivastava, Sharp coefficient estimates for a certain general class of spirallike functions by means of differential subordination, Filomat, 27, 1351-1356, 2013.

Year 2024, Volume: 53 Issue: 1, 53 - 61, 29.02.2024

Tuğba Yavuz Şahsene Altınkaya

https://doi.org/10.15672/hujms.1180981

Abstract

References

  • [1] O. Ahuja and A. Çetinkaya, Use of quantum calculus approach in mathematical sciences and its role in geometric function theory, AIP Conference Proceedings, 2095 (1), 1-14, 2019.
  • [2] O. Ahuja, A. Çetinkaya and N. K. Jain, Analytic functions with conic domains associated with certain generalized $q$-integral operator, arXiv preprint arXiv:2012.13776.
  • [3] S. Altınkaya, On the inclusion properties for $\vartheta $-spirallike functions involving both Mittag-Leffler and Wright function, Turkish J. Math. 46 (3), 1119-1131, 2022.
  • [4] M. K. Aouf and T. M. Seoudy, Convolution properties for classes of bounded analytic functions with complex order defined by $q$-derivative operator, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 113 (2), 1279-1288, 2019.
  • [5] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135, 429–446, 1969.
  • [6] S. Bulut, Certain subclasses of analytic and bi-univalent functions involving the $q$-derivative operator, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 66 (1), 108- 114, 2017.
  • [7] G. Gasper and M. Rahman, Basic hypergeometric series, second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  • [8] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving $q$-calculus,Anal. Math. 43 (3), 475-487, 2017.
  • [9] F. H. Jackson, On $q$-functions and a certain difference operator, Earth Environ. Sci. Trans. R. Soc. Edinb. 46, 253–281, 1908.
  • [10] F. H. Jackson, On $q$-definite integrals, Q. J. Pure Appl. Math. 14, 193-203, 1910.
  • [11] S. Mahmood, N. Raza, E. S. A. Abujarad, G. Srivastava, H. M. Srivastava, S. N. Malik, Geometric properties of certain classes of analytic functions associated with $q$-integral operators, Symmetry, 11 (5), 1-14, 2019.
  • [12] N. Mustafa and S. Korkmaz, The sharp inequality for the coefficients of certain subclass of analytic functions defined by $q$-derivative, Journal of Scientific and Engineering Research 7 (4), 209-218, 2020.
  • [13] K. I. Noor, S. Riaz and M. A. Noor, On $q$-Bernardi integral operator, TWMS J. Pure Appl. Math. 8 (1), 3–11, 2017.
  • [14] S. D. Purohit and R. K. Raina, Certain subclasses of analytic functions associated with fractional $q$-calculus operators, Math. Scand. 109 (1), 55-70, 2011.
  • [15] M. Raza, H. M. Srivastava, M. Arif and K. Ahmad, Coefficient estimates for a certain family of analytic functions involving a $q$-derivative operator, Ramanujan J. 55 (1), 53-71, 2022.
  • [16] Z. Shareef, S. Hussain and M. Darus, Convolution operators in the geometric function theory, J. Inequal. Appl. 2012 (213), 1-11, 2012.
  • [17] H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 1, 48-61, 1985.
  • [18] L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky, 62, 12–19, 1933.
  • [19] H. M. Srivastava, 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.
  • [20] H. M. Srivastava, 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. A Sci. 44 (1), 327-344, 2020.
  • [21] Q. H. Xu, C. B. Lv, N. C. Luo and H. M. Srivastava, Sharp coefficient estimates for a certain general class of spirallike functions by means of differential subordination, Filomat, 27, 1351-1356, 2013.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Tuğba Yavuz 0000-0002-0490-9313

Şahsene Altınkaya 0000-0002-7950-8450

Early Pub Date January 10, 2024
Publication Date February 29, 2024
Published in Issue Year 2024 Volume: 53 Issue: 1

Cite

APA Yavuz, T., & Altınkaya, Ş. (2024). Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics, 53(1), 53-61. https://doi.org/10.15672/hujms.1180981
AMA Yavuz T, Altınkaya Ş. Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics. February 2024;53(1):53-61. doi:10.15672/hujms.1180981
Chicago Yavuz, Tuğba, and Şahsene Altınkaya. “Notes on Some Classes of Spirallike Functions Associated With the $q$-Integral Operator”. Hacettepe Journal of Mathematics and Statistics 53, no. 1 (February 2024): 53-61. https://doi.org/10.15672/hujms.1180981.
EndNote Yavuz T, Altınkaya Ş (February 1, 2024) Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics 53 1 53–61.
IEEE T. Yavuz and Ş. Altınkaya, “Notes on some classes of spirallike functions associated with the $q$-integral operator”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, pp. 53–61, 2024, doi: 10.15672/hujms.1180981.
ISNAD Yavuz, Tuğba - Altınkaya, Şahsene. “Notes on Some Classes of Spirallike Functions Associated With the $q$-Integral Operator”. Hacettepe Journal of Mathematics and Statistics 53/1 (February 2024), 53-61. https://doi.org/10.15672/hujms.1180981.
JAMA Yavuz T, Altınkaya Ş. Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics. 2024;53:53–61.
MLA Yavuz, Tuğba and Şahsene Altınkaya. “Notes on Some Classes of Spirallike Functions Associated With the $q$-Integral Operator”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, 2024, pp. 53-61, doi:10.15672/hujms.1180981.
Vancouver Yavuz T, Altınkaya Ş. Notes on some classes of spirallike functions associated with the $q$-integral operator. Hacettepe Journal of Mathematics and Statistics. 2024;53(1):53-61.

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