[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.
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.
[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.
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.