Certain subclasses of harmonic starlike functions associated with \(q\)− Mittag-Leffler function
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DOI:
https://doi.org/10.26637/MJM0803/0045Abstract
A new subclass of harmonic starlike functions defined by an operator which is related to \(q\)-Mittag-Leffler function. By defining this class we obtain coefficient estimates, distortion theorems, extreme points, conditions for convolution functions and convex combination are determined. Moreover, the properties of the class preserving under certain operators like the generalized Bernardi- integral operator and the \(q\)-Jackson integral operator are studied.
Keywords:
Harmonic function, analytic function, univalent function, starlike domain, convex domain, convolutionMathematics Subject Classification:
Mathematics- Pages: 988-1000
- Date Published: 01-07-2020
- Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)
Om. P. Ahuja, Planar harmonic univalent and related mappings, J. Inequal. Pure Appl. Math., 6(4)(2005), 18 pp.
Om. P. Ahuja, Recent advances in the theory of harmonic univalent mappings in the plane, Math. Student, 83(14)(2014), 125-154.
O. P. Ahuja, R. Aghalary and S. B. Joshi, Harmonic univalent functions associated with $K$-uniformly starlike functions, Math. Sci. Res. J., 9(1)(2005), 9-17.
Om. P. Ahuja, A. Çetinkaya and V. Ravichandran, Harmonic univalent functions defined by post quantum calculus operators, Acta Univ. Sapientiae Math., 11(1)(2019), $5-17$.
H.A. Al-Kharsani and R.A. Al-Khal, Univalent harmonic functions, J. Ineq. Pure Appl. Math., 8(2)(2007), 1-8.
F. M. Al-Oboudi, On univalent functions defined by a generalized Sălăgean operator, Internat. J. Math. Math. Sci., 27(2004), 1429-1436.
Y. Avc1 and E. Złotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 44(1990), 1-7.
J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9(1984), 3-25.
K. K. Dixit and S. Porwal, Convolution of the subclass of Salagean-type harmonic univalent functions with negative coefficients, Gen. Math., 18(3)(2010), 59-64.
K. K. Dixit, A. L. Pathak, S. Porwal and R. Agarwal, On a subclass of harmonic univalent functions defined by convolution and integral convolution, Int. J. Pure Appl.Math., 69(3)(2011), 255-264.
K.K. Dixit, A.L. Pathak, S. Porwal and S.B.Joshi, A family of harmonic univalent functions associated with a convolution operator, Mathematica, 53(76)(1)(2011), $35-44$
K. K. Dixit and S. Porwal, Some properties of harmonic functions defined by convolution, Kyungpook Math. J., $49(4)(2009), 751-761$.
S. Elhaddad, H. Aldweby and M. Darus, Neighborhoods of certain classes of analytic functions defined by a generalized differential operator involving Mittag-Leffler function, Acta Univ. Apulensis Math. Inform., 55(2018), 1-10.
S. Elhaddad, H. Aldweby, M. Darus, On a subclass of harmonic univalent functions involving a new operator containing q-Mittag-Leffler function, International Journal of Mathematics and Computer Science, 14(4)(2019), 833-847.
${ }^{[15]}$ B. A. Frasin, Comprehensive family of harmonic univalent functions, SUT J. Math., 42(1)(2006), 145-155.
B. A. Frasin and N. Magesh, Certain subclasses of uniformly harmonic $beta$-starlike functions of complex order, Stud. Univ. Babeş-Bolyai Math., 58(2)(2013), 147-158.
F. H. Jackson, $q$-Difference Equations, Amer. J. Math., 32(4)(1910), 305-314.
Y. C. Kim, J. M. Jahangiri and J. H. Choi, Certain convex harmonic functions, Int. J. Math. Math. Sci., 29(8)(2002), 459-465.
J. M. Jahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 52(2)(1998), 57-66.
J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235(2)(1999), 470-477.
J. M. Jahangiri, Harmonic univalent functions defined by $q$ - calculus operators, Intern. J. Math. Anal. Appl., $5(2)(2018), 39-43$.
J. M. Jahangiri, N. Magesh and C. Murugesan, Certain subclasses of starlike harmonic functions defined by subordination, J. Fract. Calc. Appl., 8(2)(2017), 88-100.
N. Magesh and S. Porwal, Harmonic uniformly $beta$-starlike functions defined by convolution and integral convolution, Acta Univ. Apulensis Math. Inform., 32(2012), 127-139.
N. Magesh, S. Porwal and V. Prameela, Harmonic uniformly $beta$-starlike functions of complex order defined by convolution and integral convolution, Stud. Univ. BabeşBolvai Math 59(2)(2014) 177-190.
T. Rosy, S. B. Adolph, K. G. Subramanian and J. M. Jahangiri, Goodman-Rønning-type harmonic univalent functions, Kyungpook Math. J., 41(1)(2001), 45-54.
G. S. Sălăgean, Subclasses of univalent functions, Complex Analysis Fifth Romanian-Finnish Sem., Part. 1(Bucharest, 1981), Lecture Notes in Math., vol. 1013, Springer, Berlin (1983), 367-372.
S. K. Sharma, R. Jain, On some properties of generalized q-Mittag- Leffler function, Mathematica Aeterna, $4(6)(2014), 613-619$.
H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., 220(1)(1998), $283-289$.
H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math., 28(2)(1999), 275-284.
H. M. Srivastava, B. A. Frasin, V. Pescar, Univalence of integral operators involving Mittag- Leffler functions, Appl. Math. Inf. Sci., 11(3)(2017), 635-641.
K. G. Subramanian, T. V. Sudharsan, A. B. Stephen, and J. M. Jahangiri, A note on Salagean-type harmonic univalent functions, Gen. Math., 16(3)(2008), 29-40.
A. Wiman, Über den Fundamental satz in der Theorie der Funktionen $E_alpha(x)$, Acta Mathematica, 29(1)(1905), 191-201.
$left[right.$ [3] A. Wiman, Uber die Nullstellun der Funktionen $E_alpha(x)$, Acta Mathematica, 29(1)(1905), 217-234.
S. Yalçin, M. Öztürk and M. Yamankaradeniz, On the subclass of Salagean-type harmonic univalent functions, J. Inequal. Pure Appl. Math., 8(2)(2007), 9 pp.
S. Yalçin, A new class of Salagean-type harmonic univalent functions, Appl. Math. Lett., 18(2)(2005), 191-198.
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