Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 89 -- 98

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This work is licensed under a Creative Commons Attribution 4.0 International License.

SUBCLASSES OF MEROMORPHIC p-VALENT FUNCTIONS DEFINED BY q-DERIVATIVE OPERATOR ASSOCIATED WITH CASSINIAN OVALS

Amit Soni, Matri Dutt Sharma and Prem Pratap Vyas

Abstract. In the present investigation we introduce two new subclasses MS*q( p,b; c) and MKq(p,b; c) of meromorphic multivalent functions by using q-derivative operator defined in the punctured unit disc. We use the Cassinian Oval √(1+cz) with c∈(0,1] as a subordinant function in this treatise. Also we derive several properties including convolution properties, the necessary and sufficient condition and coefficient estimates for these subclasses.

2020 Mathematics Subject Classification: 30C45
Keywords: Meromorphic p-valent functions, Hadamard product (or convolution), Subordination between analytic functions, q-derivative operator, Cassinian ovals.

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References

  1. S. Agrawal and S.K. Sahoo, A generalization of starlike functions of order α, Hokkaido Math. J., 46(2017), 15-27. MR3677873. Zbl 1361.30017

  2. M.K. Aouf, J. Dziok and J. Sokol, On a subclass of strongly starlike functions, Appl. Math. Letters, \bf24 (2011), 27-32. MR2727984. Zbl 1202.30014.

  3. M.K. Aouf, A.O. Mostafa and H.M. Zayed, Convolution properties for some subclasses of meromorphic functions of complex order, Abstr. Appl. Anal., (2015), 6pages, Article ID 973613.MR3378565. Zbl 1433.30028.

  4. N.E. Cho, V. Kumar, O.S. Kwon and Y.J. Sim, Coefficient bounds for certain subclasses of starlike functions, J. Inequal. Appl. 2019 (2019) :276 13 pages. https://doi.org/10.1186/s13660-019-2231-3. MR4025537.

  5. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.

  6. F.H. Jackson, On q-functions and a certain difference operator, Trans. R. Soc. Edinb., 46(2)(1909), 253-281.

  7. F.H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41(1910), 193-203. JFM 41.0317.04.

  8. F.H. Jackson, q-difference equations, Amer. J. Math., 32(1910), 305-314. MR1506108.

  9. S. Kant and P. P. Vyas, Convolution properties for certain subclasses of meromorphic p-valent functions, J. Fract. Calc. Appl. 12(2)(2021), 197-203.

  10. R. Kargar and L. Trojnar-Spelina, Some applications of differential subordination for certain starlike functions, Turkish J. Math. 43 4(2019), 1979-1987. MR3992664. Zbl 1433.30037.

  11. E. Niczyporowicz , Krzywe plaskie, PWN, Warszawa 1991.

  12. S.D. Purohit and R.K. Raina, Certain subclasses of analytic functions associated with fractional q-calculus operators, Math. Scand., 109(1)(2011), 55-70. MR2831147. Zbl 1229.33027.

  13. R.K. Raina and J. Sokol, On a class of analytic functions governed by subordination, Acta Univ. Sapientiae Math., 11(1) (2019), 144-155. MR3995744. Zbl 1432.30013.

  14. R.K. Raina, P. Sharma and J. Sokol, Certain classes of analytic functions related to the Crescent-Shaped regions, J. Contemp. Mathemat. Anal., (53)(2018), 355-362. MR3900220. Zbl 1428.30022.

  15. T.M. Seoudy, Classes of analytic functions associated with certain integral operator, Electron. J. Math. Anal. Appl., 4(2)(2016), 254-258. Zbl 06778612.

  16. T.M. Seoudy and M.K. Aouf, Convolution properties for certain classes of analytic functions defined by q-derivative operator, Abstr. Appl. Anal., (2014), 7pages, Article ID 846719. MR3272218 . Zbl 07023188.

  17. H. Shamsan and S. Latha, On generalized bounded mocanu variation related to q-derivative and conic regions, Annals of Pure and Applied Mathematics, 17(1)(2018), 67-83.

  18. J. Sokol, Coefficient estimates in a class of strongly starlike functions, Kyungpook Math. J., \bf49 (2009), 349-353. MR2554891. Zbl 1176.30068.

  19. H.M. Srivastava, Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A Sci., 44(1)(2020), 327-344.

  20. H.M. Srivastava and D. Bansal, Close-to-convexity of a certain family of q-Mittag-Leffler functions, J. Nonlinear Var. Anal., 1(2017), 61-69. Zbl 1400.30035.

  21. R. Srivastava and H.M. Zayed, Subclasses of analytic functions of complex order defined by q-derivative operator, Stud. Univ. Babeş-Bolyai Math., 64(1)(2019), 71-80. MR3928603. Zbl 1438.30099.

  22. Y. Yunus, A.B. Akbarally and S.A. Halim, On a subclass of starlike functions associated with generalized cardioid, Int. J. Appl. Math., \bf33(5) (2020), 765-782.

  23. H.M. Zayed and M.K. Aouf, Subclasses of analytic functions of complex order associated with q-mittag leffler function, J. Egyptian Math. Soc., 26(2)(2018), 278-286. MR4092168. Zbl 1435.30071.




Amit Soni
Department of Mathematics,
Government Engineering College,
Bikaner-334001, INDIA
e-mail: aamitt1981@gmail.com

Matri Dutt Sharma
Department of Physics,
Government Dungar College,
Bikaner-334003, INDIA
e-mail: mdsharma.phy@gmail.com


Prem Pratap Vyas
Department of Mathematics,
Government Dungar College,
Bikaner-334003, INDIA
e-mail: prempratapvyas@gmail.com

http://www.utgjiu.ro/math/sma