Certain class of analytic functions dened by \(q\)-analogue of Ruscheweyh dierential operator

Mohamad K. Aouf, Adela O. Mostafa, Fawziah Y. Alquhali

Abstract


In this paper, we obtain coefficient estimates, distortion theorems, radii of close-to-convexity, starlikeness and convexity for functions belonging to the class \(TB_{q}^{λ}(α,β)\) of analytic starlike and convex functions defined by q-analogue of Ruscheweyh differential operator. Also we find closure theorems, \(N_{k,q,δ}(e,g)\) neighbourhood and partial sums for functions in this class.

Keywords


Analytic functions, Coefficient estimates, Distortion, q-Ruscheweyh type defferential operator, Neighbourhoods, Partial sums.

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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.

Annby, M. H., Mansour, Z. S., q-Fractional Calculas 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. 2006, Article ID38258, (2006), 1-6.

Aouf, M. K., Neighborhoods of certain p-valently analytic functions defined by using Sălăgean 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, and G. S. Sălăgean, On a generalization of starlike functions with negative coefficients, Math., Tome 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., Seoudy, T. M., Convolution properties for classes of bounded analytic functions with complex order defined by q-derivative operator, Rav. 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 of analytic functions difined by Dziok-Srivastava operator, Acta Univ. Apulensis, (2012), no. 30, 65-76.

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-Calculas 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, Combridge Univ. Press, Cambrididge, 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.

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

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., 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-Calculas and associated Fake-Szego problem for p-valently q-starlike functions and p-valently q-convex functions of complex order, Miskole Math. Notes, 20(2019), no. 1, 489-509.




DOI: http://dx.doi.org/10.24193/subbmath.2024.1.03

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