Notes on some classes of spirallike functions associated with the $q$-integral operator
Year 2024,
, 53 - 61, 29.02.2024
Tuğba Yavuz
,
Şahsene Altınkaya
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.
References
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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.
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Mittag-Leffler and Wright function, Turkish J. Math. 46 (3), 1119-1131, 2022.
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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.
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135, 429–446, 1969.
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conic domains involving $q$-calculus,Anal. Math. 43 (3), 475-487, 2017.
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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.
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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,
, 53 - 61, 29.02.2024
Tuğba Yavuz
,
Şahsene Altınkaya
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.