TY - JOUR T1 - Classes of harmonic starlike functions defined by Sălăgean-type $q$-differential operators AU - Jahangiri, Jay M. AU - Murugusundaramoorthy, Gangadharan AU - Vijaya, Kaliappan PY - 2020 DA - February DO - 10.15672/hujms.568306 JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 416 EP - 424 VL - 49 IS - 1 LA - en AB - Sufficient and necessary coefficient bounds, extreme points of closed convex hulls, anddistortion theorems are determined for a family of harmonic starlike functions of complex order involving Sălăgean-type $q$-differential operators. KW - Harmonic univalent functions KW - q-calculus KW - Sălăgean-type differential operators CR - [1] A. Aral, V. Gupta and R.P. Agarwal, Applications of q-calculus in operator theory, Springer, New York, 2013. CR - [2] Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie- Sklodowska Sect. A, 44, 1–7, 1990. CR - [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. CR - [4] J. Clunie and T. Sheil-Small, Harmonic univalent Functions, Ann. Acad. Aci. Fenn. Ser. A.I. Math. 9, 3–25, 1984. CR - [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. CR - [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. CR - [7] F.H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46, 253–281, 1908. CR - [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. CR - [9] J.M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl. 235, 470–477, 1999. CR - [10] J.M. Jahangiri, Harmonic univalent functions defined by q− calculus operators, Inter. J. Math. Anal. Appl. 5 (2), 39–43, 2018. CR - [11] J.M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Sălăgean-Type harmonic univalent functions, Southwest J. Pure Appl. Math. 2, 77–82, 2002. CR - [12] J.M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, Starlikeness of Rucheweyh type harmonic univalent functions, J. Indian Acad. Math. 26, 191–200, 2004. CR - [13] S. Kanas, and D. Răducanu, Some subclass of analytic functions related to conic domains, Math. Slovaca, 64 (5), 1183–1196, 2014. CR - [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. CR - [15] G.F. Sălăgean, Subclasses of univalent functions, Springers-Verlog 1013, 362–372, 1983. CR - [16] H. Silverman, Harmonic univalent functions with negative coefficients , J. Math. Anal. Appl. 220, 283–289, 1998. UR - https://doi.org/10.15672/hujms.568306 L1 - https://dergipark.org.tr/en/download/article-file/720144 ER -