Certain Subclasses Of Harmonic Starlike Functions Associated With q-Analouge Of Ruscheweyh Operator
Keywords:
Harmonic function, analytic function, univalent function, starlike domain, convex domain, convolution .
Abstract
In this work, we introduce and study a subclass of harmonic uniformly β - starlike functions defined by q-analogue of Ruscheweyh derivative operator. Coefficient bounds, extreme points, distortion bounds, convolution conditions and convex combination are determined for functions in this class. Also, properties of the class preserving under. The generalized Bernardi-Libera –Livingston integral operator and the q-Jackson integral operator are discussed. Furthermore, many of our results are either extensions or new approaches to those corresponding to previously known results.
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References
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[23] G. Murugusundaramoorthy, On a class of Ruschewey-type harmonic univalent functions with varying arguments, Southwest J. Pure Appl. Math., 2:90-95, 2003.
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functions, Kyungpook Math. J. 41 (2001), no. 1, 45-54.
[26] S. Ruscheweyh, New criteria for univalent functions, Proceedings of the American Mathematical Society, 49(1975), 109-115.
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283-289.
[28] H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math. 28 (1999),
no. 2, 275-284.
[29] S. Yalcin, M. Ozturk and M. Yamankaradeniz, A subclass of harmonic univalent functions with negative coefficients, Appl. Math. Comp. 142 (2003), 469 -476.
[2] Om. P. Ahuja, Recent advances in the theory of harmonic univalent mappings in the plane, Math. Student 83 (2014), no. 1-4, 125-154.
[3] O. P. Ahuja, R. Aghalary and S. B. Joshi, Harmonic univalent functions associated with K-uniformly starlike functions, Math. Sci. Res. J. 9 (2005), no. 1, 9-17.
[4] Om. P. Ahuja, A. C etinkaya and V. Ravichandran, Harmonic univalent functions dened by post quantum calculus operators, Acta Univ. Sapientiae Math. 11 (2019), no. 1, 5-17.
[5] H. Aldweby and M. Darus, Some subordination results on q-analogue of Ruscheweyh dierential operator, Abstract and Applied Analysis, 2014(2014), Article ID 958563, 6 pages.
[6] H.A. Al-Kharsani and R.A. Al-Khal, Univalent harmonic functions, J. Ineq. Pure Appl. Math., 8(2):1{8, 2007.
[7] Y. Avc and E. Z lotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sk lodowska Sect. A 44 (1990), 1-7.
[8] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25.
[9] K. K. Dixit, A. L. Pathak, S. Porwal and R. Agarwal, On a subclass of harmonic univalent functions dened by convolution and integral convolution, Int. J. Pure Appl. Math. 69 (2011), no. 3, 255-264.
[10] 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) (2011), no. 1, 35-44.
[11] K. K. Dixit and S. Porwal, Some properties of harmonic functions dened by convolution, Kyungpook Math. J. 49 (2009), no. 4, 751-761.
[12] S. Elhaddad, H. Aldweby and M. Darus, Some properties on a class of harmonic univalent functions dened byq-analogue of Ruscheweyh operator, J. Math. Anal. 9 (2018), no. 4, 28-35.
[13] B. A. Frasin, Comprehensive family of harmonic univalent functions, SUT J. Math. 42 (2006), no. 1, 145-155.
[14] B. A. Frasin and N. Magesh, Certain subclasses of uniformly harmonic -starlike functions of complex order, Stud. Univ. Babes-Bolyai Math. 58 (2013), no. 2, 147-158.
[15] F. H. Jackson, q-Dierence Equations, Amer. J. Math. 32 (1910), no. 4, 305{314.
[16] Y. C. Kim, J. M. Jahangiri and J. H. Choi, Certain convex harmonic functions, Int. J. Math. Math. Sci. 29
(2002), no. 8, 459-465.
[17] J. M. Jahangiri, Coecient bounds and univalence criteria for harmonic functions with negative coefficients, Ann.
Univ. Mariae Curie-Sk lodowska Sect. A 52 (1998), no. 2, 57-66.
[18] J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), no. 2, 470-477.
[19] J. M. Jahangiri, Harmonic univalent functions dened by q- calculus operators, Intern. J. Math. Anal. Appl., 5
(2018), no. 2, 39-43
[20] J. M. Jahangiri, N. Magesh and C. Murugesan, Certain subclasses of starlike harmonic functions dened by subordination, J. Fract. Calc. Appl. 8 (2017), no. 2, 88-100.
[21] N. Magesh and S. Porwal, Harmonic uniformly -starlike functions dened by convolution and integral convolution, Acta Univ. Apulensis Math. Inform. No. 32 (2012), 127-139.
[22] N. Magesh, S. Porwal and V. Prameela, Harmonic uniformly -starlike functions of complex order dened by
convolution and integral convolution, Stud. Univ. Babes-Bolyai Math. 59 (2014), no. 2, 177-190.
[23] G. Murugusundaramoorthy, On a class of Ruschewey-type harmonic univalent functions with varying arguments, Southwest J. Pure Appl. Math., 2:90-95, 2003.
[24] S. Porwal, K. K. Dixit, V. Kumar, A.L. Pathak and P. Dixit, A New Subclass of Harmonic Univalent Functions
dened by Dziok-Srivastava Operator, Advances in Theoretical and Applied Mathematics, Volume 5, Number 1
(2010), pp. 109-119.
[25] T. Rosy, S. B. Adolph, K. G. Subramanian and J. M. Jahangiri, Goodman-Rnning-type harmonic univalent
functions, Kyungpook Math. J. 41 (2001), no. 1, 45-54.
[26] S. Ruscheweyh, New criteria for univalent functions, Proceedings of the American Mathematical Society, 49(1975), 109-115.
[27] H. Silverman, Harmonic univalent functions with negative coecients, J. Math. Anal. Appl. 220 (1998), no. 1,
283-289.
[28] H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math. 28 (1999),
no. 2, 275-284.
[29] S. Yalcin, M. Ozturk and M. Yamankaradeniz, A subclass of harmonic univalent functions with negative coefficients, Appl. Math. Comp. 142 (2003), 469 -476.
Published
2020-08-20
How to Cite
Swamy, S. R., & Mamatha, P. (2020). Certain Subclasses Of Harmonic Starlike Functions Associated With q-Analouge Of Ruscheweyh Operator. Journal of Progressive Research in Mathematics, 16(4), 3109-3121. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1884
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