A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator

Zhi-gang Wang; Saqib Hussain; Muhammad Naeem; Tahir Bakhat; Shahid Khan

doi:10.15672/hujms.576878

Research Article

A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator

Year 2020, Volume: 49 Issue: 4, 1471 - 1479, 06.08.2020

Zhi-gang Wang , Saqib Hussain , Muhammad Naeem , Tahir Bakhat Shahid Khan

https://doi.org/10.15672/hujms.576878

Cited By: 12

Abstract

The main objective of the present paper is to define a subclass $Q_{q}(\lambda,\mu,A,B)$ of analytic functions by using subordination along with the newly defined $q$-analogue of Choi-Saigo-Srivastava operator. Such results as coefficient estimates, integral representation, linear combination, weighted and arithmetic means, and radius of starlikeness for this class are derived.

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Keywords

analytic functions, univalent functions, $q$-differential operator, $q$-analogue of Choi-Saigo-Srivastava operator

References

[1] H. Aldweby and M. Darus, Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal. 2014, 1–9, 2014.
[2] F.M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 2004, 1419–1436, 2004.
[3] F.M. Al-Oboudi, On classes of functions related to starlike functions with respect to symmetric conjugate points defined by a fractional differential operator, Complex Anal. Oper. Theory, 5, 647–658, 2011.
[4] F.M. Al-Oboudi and K.A. Al-Amoudi, On classes of analytic functions related to conic domains, J. Math. Anal. Appl. 399, 655–667, 2008.
[5] G.A. Anastassiou and S.G. Gal, Geometric and approximation properties of generalized singular integrals in the unit disk, J. Korean Math. Soc. 23, 425–443, 2006.
[6] A. Aral, On the generalized Picard and Gauss Weierstrass singular integrals, J. Comput. Anal. Appl. 8, 249–261, 2006.
[7] A. Aral, On the generalized Picard and Gauss Weierstrass singular integrals, J. Comput. Anal. Appl. 8, 249–261, 2006.
[8] A. Aral and V. Gupta, On q-Baskakov type operators, Demonstr. Math. 42, 109–122, 2009.
[9] A. Aral and V. Gupta, Generalized q-Baskakov operators, Math. Slovaca, 61, 619–634, 2011.
[10] S.Z.H. Bukhari, M. Nazir, and M. Raza, Some generalisations of analytic functions with respect to 2k-symmetric conjugate points, Maejo Int. J. Sci. Technol. 10, 1–12, 2016.
[11] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Anal. Math. 43, 475–487, 2017.
[12] S. Hussain, S. Khan, M.A. Zaighum, and M. Darus, Applications of a q-Salagean type operator on multivalent functions, J. Inequal. Appl. 2018, Art. 301, 2018.
[13] F.H. Jackson, On q-functions and a certain difference operator, Earth Environ. Sci. Tran. R. Soc. Edinb. 46, 253–281, 1909.
[14] F.H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math. 41, 193–203, 1910.
[15] W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28, 297–326, 1973.
[16] S. Kanas and D. Raducanu, Some class of analytic functions related to conic domains, Math. Slovaca, 64, 1183–1196, 2014.
[17] M.-S. Liu, On a subclass of p-valent close to convex functions of type α and order β, J. Math. Study 30, 102–104, 1997.
[18] S. Mahmood and J. Sokol, New subclass of analytic functions in conical domain associated with Ruscheweyh q-differential operator, Results Math. 71, 1–13, 2017.
[19] M. Naeem, S. Hussain, T. Mahmood, S. Khan, and M. Darus, A new subclass of analytic functions defined by using Salagean q-differential operator, Mathematics, 7, 458–469, 2019.
[20] K.I. Noor, On new classes of integral operator, J. Natur. Geom. 16, 71–80, 1999.
[21] K.I. Noor and M. A. Noor, On integral operators, J. Math. Anal. Appl. 238, 341–352, 1999.
[22] K.I. Noor, N. Khan, and Q.Z. Ahmad, Some properties of multivalent spiral-like functions, Maejo Int. J. Sci. Technol. 12, 139–151, 2018.
[23] M. Sabil, Q.Z. Ahmad, B. Khan, M. Tahir, and N. Khan, Generalisation of certain subclasses of analytic and bi-univalent functions, Maejo Int. J. Sci. Technol. 13, 1–9, 2019.
[24] F.M. Sakar and S.M. Aydoˇgan, Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions, Appl. Math. Comput. 319, 461–468, 2018.
[25] F.M. Sakar and S.M. Aydoˇgan, Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions defined by convolution, Acta Univ. Apulensis Math. Inform. 55, 11–21, 2018.
[26] Z. Shareef, S. Hussain, and M. Darus, Convolution operator in geometric functions theory, J. Inequal. Appl. 2012, Art. 213, 2012.
[27] H.M. Srivastava, S. Khan, Q.Z. Ahmad, N. Khan, and S. Hussain, The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator, Stud. Univ. Babes-Bolyai Math. 63, 419–436, 2018.

Year 2020, Volume: 49 Issue: 4, 1471 - 1479, 06.08.2020

Zhi-gang Wang , Saqib Hussain , Muhammad Naeem , Tahir Bakhat Shahid Khan

https://doi.org/10.15672/hujms.576878

Cited By: 12

Abstract

References

[1] H. Aldweby and M. Darus, Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal. 2014, 1–9, 2014.
[2] F.M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 2004, 1419–1436, 2004.
[3] F.M. Al-Oboudi, On classes of functions related to starlike functions with respect to symmetric conjugate points defined by a fractional differential operator, Complex Anal. Oper. Theory, 5, 647–658, 2011.
[4] F.M. Al-Oboudi and K.A. Al-Amoudi, On classes of analytic functions related to conic domains, J. Math. Anal. Appl. 399, 655–667, 2008.
[5] G.A. Anastassiou and S.G. Gal, Geometric and approximation properties of generalized singular integrals in the unit disk, J. Korean Math. Soc. 23, 425–443, 2006.
[6] A. Aral, On the generalized Picard and Gauss Weierstrass singular integrals, J. Comput. Anal. Appl. 8, 249–261, 2006.
[7] A. Aral, On the generalized Picard and Gauss Weierstrass singular integrals, J. Comput. Anal. Appl. 8, 249–261, 2006.
[8] A. Aral and V. Gupta, On q-Baskakov type operators, Demonstr. Math. 42, 109–122, 2009.
[9] A. Aral and V. Gupta, Generalized q-Baskakov operators, Math. Slovaca, 61, 619–634, 2011.
[10] S.Z.H. Bukhari, M. Nazir, and M. Raza, Some generalisations of analytic functions with respect to 2k-symmetric conjugate points, Maejo Int. J. Sci. Technol. 10, 1–12, 2016.
[11] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Anal. Math. 43, 475–487, 2017.
[12] S. Hussain, S. Khan, M.A. Zaighum, and M. Darus, Applications of a q-Salagean type operator on multivalent functions, J. Inequal. Appl. 2018, Art. 301, 2018.
[13] F.H. Jackson, On q-functions and a certain difference operator, Earth Environ. Sci. Tran. R. Soc. Edinb. 46, 253–281, 1909.
[14] F.H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math. 41, 193–203, 1910.
[15] W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28, 297–326, 1973.
[16] S. Kanas and D. Raducanu, Some class of analytic functions related to conic domains, Math. Slovaca, 64, 1183–1196, 2014.
[17] M.-S. Liu, On a subclass of p-valent close to convex functions of type α and order β, J. Math. Study 30, 102–104, 1997.
[18] S. Mahmood and J. Sokol, New subclass of analytic functions in conical domain associated with Ruscheweyh q-differential operator, Results Math. 71, 1–13, 2017.
[19] M. Naeem, S. Hussain, T. Mahmood, S. Khan, and M. Darus, A new subclass of analytic functions defined by using Salagean q-differential operator, Mathematics, 7, 458–469, 2019.
[20] K.I. Noor, On new classes of integral operator, J. Natur. Geom. 16, 71–80, 1999.
[21] K.I. Noor and M. A. Noor, On integral operators, J. Math. Anal. Appl. 238, 341–352, 1999.
[22] K.I. Noor, N. Khan, and Q.Z. Ahmad, Some properties of multivalent spiral-like functions, Maejo Int. J. Sci. Technol. 12, 139–151, 2018.
[23] M. Sabil, Q.Z. Ahmad, B. Khan, M. Tahir, and N. Khan, Generalisation of certain subclasses of analytic and bi-univalent functions, Maejo Int. J. Sci. Technol. 13, 1–9, 2019.
[24] F.M. Sakar and S.M. Aydoˇgan, Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions, Appl. Math. Comput. 319, 461–468, 2018.
[25] F.M. Sakar and S.M. Aydoˇgan, Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions defined by convolution, Acta Univ. Apulensis Math. Inform. 55, 11–21, 2018.
[26] Z. Shareef, S. Hussain, and M. Darus, Convolution operator in geometric functions theory, J. Inequal. Appl. 2012, Art. 213, 2012.
[27] H.M. Srivastava, S. Khan, Q.Z. Ahmad, N. Khan, and S. Hussain, The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator, Stud. Univ. Babes-Bolyai Math. 63, 419–436, 2018.

There are 27 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Mathematics
Authors	Zhi-gang Wang 0000-0001-6118-7196 Saqib Hussain Muhammad Naeem Tahir Bakhat This is me Shahid Khan This is me
Publication Date	August 6, 2020
Published in Issue	Year 2020 Volume: 49 Issue: 4

Cite

APA	Wang, Z.-g., Hussain, S., Naeem, M., Bakhat, T., et al. (2020). A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator. Hacettepe Journal of Mathematics and Statistics, 49(4), 1471-1479. https://doi.org/10.15672/hujms.576878
AMA	Wang Zg, Hussain S, Naeem M, Bakhat T, Khan S. A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator. Hacettepe Journal of Mathematics and Statistics. August 2020;49(4):1471-1479. doi:10.15672/hujms.576878
Chicago	Wang, Zhi-gang, Saqib Hussain, Muhammad Naeem, Tahir Bakhat, and Shahid Khan. “A Subclass of Univalent Functions Associated With $q$-Analogue of Choi-Saigo-Srivastava Operator”. Hacettepe Journal of Mathematics and Statistics 49, no. 4 (August 2020): 1471-79. https://doi.org/10.15672/hujms.576878.
EndNote	Wang Z-g, Hussain S, Naeem M, Bakhat T, Khan S (August 1, 2020) A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator. Hacettepe Journal of Mathematics and Statistics 49 4 1471–1479.
IEEE	Z.-g. Wang, S. Hussain, M. Naeem, T. Bakhat, and S. Khan, “A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, pp. 1471–1479, 2020, doi: 10.15672/hujms.576878.
ISNAD	Wang, Zhi-gang et al. “A Subclass of Univalent Functions Associated With $q$-Analogue of Choi-Saigo-Srivastava Operator”. Hacettepe Journal of Mathematics and Statistics 49/4 (August 2020), 1471-1479. https://doi.org/10.15672/hujms.576878.
JAMA	Wang Z-g, Hussain S, Naeem M, Bakhat T, Khan S. A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator. Hacettepe Journal of Mathematics and Statistics. 2020;49:1471–1479.
MLA	Wang, Zhi-gang et al. “A Subclass of Univalent Functions Associated With $q$-Analogue of Choi-Saigo-Srivastava Operator”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, 2020, pp. 1471-9, doi:10.15672/hujms.576878.
Vancouver	Wang Z-g, Hussain S, Naeem M, Bakhat T, Khan S. A subclass of univalent functions associated with $q$-analogue of Choi-Saigo-Srivastava operator. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1471-9.