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Year 2020, Volume: 49 Issue: 1, 416 - 424, 06.02.2020
https://doi.org/10.15672/hujms.568306

Abstract

References

  • [1] A. Aral, V. Gupta and R.P. Agarwal, Applications of q-calculus in operator theory, Springer, New York, 2013.
  • [2] Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie- Sklodowska Sect. A, 44, 1–7, 1990.
  • [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] J. Clunie and T. Sheil-Small, Harmonic univalent Functions, Ann. Acad. Aci. Fenn. Ser. A.I. Math. 9, 3–25, 1984.
  • [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] 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] F.H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46, 253–281, 1908.
  • [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.
  • [9] J.M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl. 235, 470–477, 1999.
  • [10] J.M. Jahangiri, Harmonic univalent functions defined by q− calculus operators, Inter. J. Math. Anal. Appl. 5 (2), 39–43, 2018.
  • [11] J.M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Sălăgean-Type harmonic univalent functions, Southwest J. Pure Appl. Math. 2, 77–82, 2002.
  • [12] J.M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Starlikeness of Rucheweyh type harmonic univalent functions, J. Indian Acad. Math. 26, 191–200, 2004.
  • [13] S. Kanas, and D. Răducanu, Some subclass of analytic functions related to conic domains, Math. Slovaca, 64 (5), 1183–1196, 2014.
  • [14] T. Rosy, B.A. Stephen, K.G. Subramanian and J.M. Jagangiri, Goodman-Rønning type harmonic univalent functions, Kyungpook Math. J. 41, 45–54, 2001.
  • [15] G.F. Sălăgean, Subclasses of univalent functions, Springers-Verlog 1013, 362–372, 1983.
  • [16] H. Silverman, Harmonic univalent functions with negative coefficients , J. Math. Anal. Appl. 220, 283–289, 1998.

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

Year 2020, Volume: 49 Issue: 1, 416 - 424, 06.02.2020
https://doi.org/10.15672/hujms.568306

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.

References

  • [1] A. Aral, V. Gupta and R.P. Agarwal, Applications of q-calculus in operator theory, Springer, New York, 2013.
  • [2] Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie- Sklodowska Sect. A, 44, 1–7, 1990.
  • [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] J. Clunie and T. Sheil-Small, Harmonic univalent Functions, Ann. Acad. Aci. Fenn. Ser. A.I. Math. 9, 3–25, 1984.
  • [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] 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] F.H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46, 253–281, 1908.
  • [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.
  • [9] J.M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl. 235, 470–477, 1999.
  • [10] J.M. Jahangiri, Harmonic univalent functions defined by q− calculus operators, Inter. J. Math. Anal. Appl. 5 (2), 39–43, 2018.
  • [11] J.M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Sălăgean-Type harmonic univalent functions, Southwest J. Pure Appl. Math. 2, 77–82, 2002.
  • [12] J.M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Starlikeness of Rucheweyh type harmonic univalent functions, J. Indian Acad. Math. 26, 191–200, 2004.
  • [13] S. Kanas, and D. Răducanu, Some subclass of analytic functions related to conic domains, Math. Slovaca, 64 (5), 1183–1196, 2014.
  • [14] T. Rosy, B.A. Stephen, K.G. Subramanian and J.M. Jagangiri, Goodman-Rønning type harmonic univalent functions, Kyungpook Math. J. 41, 45–54, 2001.
  • [15] G.F. Sălăgean, Subclasses of univalent functions, Springers-Verlog 1013, 362–372, 1983.
  • [16] H. Silverman, Harmonic univalent functions with negative coefficients , J. Math. Anal. Appl. 220, 283–289, 1998.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Jay M. Jahangiri 0000-0002-5231-3530

Gangadharan Murugusundaramoorthy 0000-0001-8285-6619

Kaliappan Vijaya This is me 0000-0002-3216-7038

Publication Date February 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 1

Cite

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