Certain class of analytic functions defined by q−analogue of Ruscheweyh differential operator

Authors

  • Mohamed K. AOUF Department of Mathematics, Faculty of Science University of Mansoura, Egypt. Email: mkaouf127@yahoo.com. https://orcid.org/0000-0001-9398-4042
  • Adela O. MOUSTAFA Department of Mathematics, Faculty of Science, University of Mansoura, Egypt. Email: adelaeg254@yahoo.com.
  • Fawziah Y. AL-QUHALI Department of Mathematics, Faculty of Education, Amran University, Yemen. Email: fyalquhali89@gmail.com. https://orcid.org/0009-0006-4628-7176

DOI:

https://doi.org/10.24193/subbmath.2024.1.03

Keywords:

Analytic functions, coefficient estimates, distortion, q−Ruscheweyh type differential operator, neighborhoods, partial sums

Abstract

In this paper, we obtain coefficient estimates, distortion theorems, radii of close-to-convexity, starlikeness and convexity for functions belonging to the class of analytic starlike and convex functions defined by q−analogue of Ruscheweyh differential operator. Also we find closure theorems, Nk,q,δ (e, g) neighborhood and partial sums for functions in this class.

Mathematics Subject Classification (2010): 30C45.

Received 07 June 2020; Accepted 06 August 2020

References

Aldweby, H., Darus, M., Some subordination results on q−analogue of Ruscheweyh differential operator, Abstract and Applied Anal. Article ID 958563, 2014(2014), 1-6.

Altinkaya, S., Magesh, N., Yalcin, S., Construction of Toeplitz matrices whose elements are the coefficients of univalent functions associated with q−derivative operator, Caspian J. Math. Sci., 8(2019), no. 1, 51-57.

Annby, M.H., Mansour, Z.S., q−Fractional Calculus Equations, Lecture Noes in Math., 2056, Springer-Verlag Berlin Heidelberg, 2012.

Aouf, M.K., On a new criterion for univalent functions of order alpha, Rend. di Mat. Roma, 11(1991), 47-59.

Aouf, M.K., Neighborhoods of certain classes of analytic functions with negative coefficients, Internat. J. Math. Math. Sci., Article ID38258, (2006), 1-6.

Aouf, M.K., Neighborhoods of certain p−valently analytic functions defined by using S˘al˘agean operator, Demonstratio Math., 41(2008), no. 3, 561-570.

Aouf, M.K., Darwish, H.E., A property of certain analytic functions involving Ruscheweyh derivatives 2, Bull. Malaysian Math. Soc., 19(1996), 9-12.

Aouf, M.K., Darwish, H.E, Sălăgean, G.S. On a generalization of starlike functions with negative coefficients, Math., 43(66)(2001), no. 1, 3-10.

Aouf, M.K., Dziok, J., Inclusion and neighborhood properties of certain subclasses of analytic and multivalent functions, European J. Pure Appl. Math., 2(2009), no. 4, 544- 553.

Aouf, M.K., Hossen, H.M., Notes on certain class of analytic functions defined by Ruscheweyh derivatives, Taiwanese J. Math., 1(1997), no. 1, 11-19.

Aouf, M.K., Mostafa, A.O., On partial sums of certain meromorphic p−valent functions, Math. Cumput. Modelling, 50(2009), no. 9-10, 1325-1331.

Aouf, M.K., Mostafa, A.O., AL-Quhali, F.Y., Properties for class of β−uniformly univalent functions defined by Sălăgean type q−difference operator, Int. J. Open Problems Complex Anal., 11(2019), no. 2, 1-16.

Aouf, M.K., Seoudy, T.M., Convolution properties for classes of bounded analytic functions with complex order defined by q−derivative operator, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., 113(2019), no. 2, 1279-1288.

Aouf, M.K., Shamandy, A., Attiyia, A.A., Certain classes of analytic and multivalent functions with negative coefficients, Tr. J. Math., 20(1996), no. 3, 353-368.

Aouf, M.K., Shamandy, A., Mostafa, A.O., Adwan, E.A., Partial sums of certain analytic functions difined by Dziok-Srivastava operator, Acta Univ. Apulensis, (2012), no. 30, 65-76.

[16] Aouf, M.K., Shamandy, A., Mostafa, A.O., Madian, S.M., Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator, Annales Univ. Mariae Curie-Sklodowska, Sectio A-Math., 54(2010), no. 1, 17-26.

Aral, A., Gupta, V., Agarwal, R.P., Applications of q−Calculus in Operator Theory, Springer, New York, NY, USA, 2013.

Attiya, A.A., Aouf, M.K., A study on certain class of analytic functions defined by Ruscheweyh derivatives, Soochow J. Math., 33(2007), no. 2, 273-289.

Frasin, B.A., Partial sums of certain analytic and univalent functions, Acta Math. Acad. Paed. Nyir, 21(2005), 135-145.

Gasper, G., Rahman, M., Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, U.K. 1990.

Goodman, A.W., Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 8(1957), 598-601.

Jackson, F.H., On q−functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46(1908), 253-281.

[23] Kanas, S., Răducanu, D., Some class of analytic functions related to conic domains, Math. Slovaca, 64(2014), no. 5, 1183-1196.

Magesh, N., Altinkaya, S., Yalcin, S., Certain subclasses of k−uniformly starlike functions associated with symmetric q−derivative operator, J. Comput. Anal. Appl., 24(2018), no. 8, 1464-1473.

Mostafa, A.O., On partial sums of certain analytic functions, Demonstratio Math., 41(2008), no. 4, 779-789.

Mostafa, A.O., Aouf, M.K., Neighborhoods of certain p−valent analytic functions of complex order, Comput. Math. Appl., 58(2009), 1183-1189.

Murugusundaramoorthy, G., Magesh, N., Linear operators associated with a subclass of uniformly convex functions, Int. J. Pure Appl. Math., 3(2006), no. 1, 123-135.

Murugusundaramoorthy, G., Srivastava, H.M., Neighborhoods of certain classes of analytic functions of complex order, J. Ineql. Pure Appl. Math., 5(2004), no. 2, Art. 24, 1-8.

Owa, S., Polatoglu, Y., Yavuz, E., Coefficient inequalities for classes of uniformly starlike and convex functions, J. Inequal. Pure Appl. Math., 7(2006), no. 5, Art. 160, 1-5.

Robertson, M.S., On the theory of univalent functions, Ann. Math., 37(1936), 374-408.

Rosy, T., Subramanian, K.G., Murugusundaramoorthy, G., Neighborhoods and partial sums of starlike functions based on Ruscheweyeh derivatives, J. Ineq. Pure Appl. Math., 4(2003), no. 4, Art., 64, 1-8.

Ruscheweyh, St., New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115.

Ruscheweyh, St., Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81(1981), 521-527.

Seoudy, T.M., Aouf, M.K., Convolution properties for certain classes of analytic functions defined by q−derivative operator, Abstract and Appl. Anal., 2014(2014), 1-7.

Seoudy, T.M., Aouf, M.K., Coefficient estimates of new classes of q−convex functions of complex order, J. Math. Ineq., 10(2016), no. 1, 135-145.

Shams, S., Kulkarni, S.R., Jahangiri, J.M., Classes of uniformly starlike and convex functions, Internat. J. Math. Math. Sci., 55(2004), 2959-2961.

Sheil-Small, T., A note on partial sums of convex schlicht functions, Bull. London Math. Soc., 2(1970), 165-168.

Silverman, H., Partial sums of starlike and convex functions, J. Math. Appl., 209(1997), 221-227.

Srivastava, M.H., Mostafa, A.O., Aouf, M.K., Zayed, H.M., Basic and fractional q−calculus and associated Fekete-Szego problem for p−valently q−starlike functions and p−valently q−convex functions of complex order, Miskolc Math. Notes, 20(2019), no. 1, 489-509.

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Published

2024-03-20

How to Cite

AOUF, M. K. ., MOUSTAFA, A. O. ., & AL-QUHALI, F. Y. . (2024). Certain class of analytic functions defined by q−analogue of Ruscheweyh differential operator. Studia Universitatis Babeș-Bolyai Mathematica, 69(1), 49–65. https://doi.org/10.24193/subbmath.2024.1.03

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