Research Article

Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators

Volume: 49 Number: 1 February 6, 2020
EN

Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators

Abstract

Sufficient and necessary coefficient bounds, extreme points of closed convex hulls, and distortion theorems are determined for a family of harmonic starlike functions of complex order involving Sălăgean-type $q$-differential operators.

Keywords

References

  1. [1] A. Aral, V. Gupta and R.P. Agarwal, Applications of q-calculus in operator theory, Springer, New York, 2013.
  2. [2] Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie- Sklodowska Sect. A, 44, 1–7, 1990.
  3. [3] T. Bulboaca, M.A. Nasr and G.F. Sălăgean, A generalization of some classes of starlike functions of complex order, Mathematica (Cluj), 34 (57), 113–118, 1992.
  4. [4] J. Clunie and T. Sheil-Small, Harmonic univalent Functions, Ann. Acad. Aci. Fenn. Ser. A.I. Math. 9, 3–25, 1984.
  5. [5] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving q-calculus, Anal. Math. 43(3)(5), 475–487, 2017.
  6. [6] S.A. Halim and A. Janteng, Harmonic functions starlike of complex order, Proc. Int. Symp. on New Development of Geometric function Theory and its Applications, 132–140, 2008.
  7. [7] F.H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46, 253–281, 1908.
  8. [8] J.M. Jahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 5 (2), 57– 66, 1998.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

February 6, 2020

Submission Date

July 5, 2018

Acceptance Date

December 21, 2018

Published in Issue

Year 2020 Volume: 49 Number: 1

APA
Jahangiri, J. M., Murugusundaramoorthy, G., & Vijaya, K. (2020). Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators. Hacettepe Journal of Mathematics and Statistics, 49(1), 416-424. https://doi.org/10.15672/hujms.568306
AMA
1.Jahangiri JM, Murugusundaramoorthy G, Vijaya K. Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):416-424. doi:10.15672/hujms.568306
Chicago
Jahangiri, Jay M., Gangadharan Murugusundaramoorthy, and Kaliappan Vijaya. 2020. “Classes of Harmonic Starlike Functions Defined by Sălăgean-Type $q$-Differential Operators”. Hacettepe Journal of Mathematics and Statistics 49 (1): 416-24. https://doi.org/10.15672/hujms.568306.
EndNote
Jahangiri JM, Murugusundaramoorthy G, Vijaya K (February 1, 2020) Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators. Hacettepe Journal of Mathematics and Statistics 49 1 416–424.
IEEE
[1]J. M. Jahangiri, G. Murugusundaramoorthy, and K. Vijaya, “Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, pp. 416–424, Feb. 2020, doi: 10.15672/hujms.568306.
ISNAD
Jahangiri, Jay M. - Murugusundaramoorthy, Gangadharan - Vijaya, Kaliappan. “Classes of Harmonic Starlike Functions Defined by Sălăgean-Type $q$-Differential Operators”. Hacettepe Journal of Mathematics and Statistics 49/1 (February 1, 2020): 416-424. https://doi.org/10.15672/hujms.568306.
JAMA
1.Jahangiri JM, Murugusundaramoorthy G, Vijaya K. Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators. Hacettepe Journal of Mathematics and Statistics. 2020;49:416–424.
MLA
Jahangiri, Jay M., et al. “Classes of Harmonic Starlike Functions Defined by Sălăgean-Type $q$-Differential Operators”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, Feb. 2020, pp. 416-24, doi:10.15672/hujms.568306.
Vancouver
1.Jay M. Jahangiri, Gangadharan Murugusundaramoorthy, Kaliappan Vijaya. Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators. Hacettepe Journal of Mathematics and Statistics. 2020 Feb. 1;49(1):416-24. doi:10.15672/hujms.568306

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