Subordination results for a class of analytic functions

M. K. Aouf; B. A. Frasin; G. Murugusundaramoorthy

doi:10.2478/mjpaa-2021-0004

Abstract

In this paper, we derive several subordination results and integral means result for certain class of analytic functions with complex order defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered

References

[1] H. Aldweby and M. Darus, Some subordination results on q -analogue of Ruscheweyh differential operator, Abst. Appl. Anal., 2014, (2014), Article ID 958563, 1-6.10.1155/2014/958563
Search in Google Scholar Back to article
[2] M. H. Annaby and Z.S.Mansour, q-Fractional Calculus and Equations, Lecture Notes in Maths, 2056, Springer-Verlag Berlin, Heidelberg 2012.10.1007/978-3-642-30898-7
Search in Google Scholar Back to article
[3] M. K. Aouf, A. Shamandy, A. O. Mostafa and F. El-Emam, Subordination results associated with b-uniformly convex and starlike functions, Proc. Pakistan Acad. Sci. 46(2),(2009), 97-101.
Search in Google Scholar Back to article
[4] M. K. Aouf, Bounded p-valent Robertson functions of order a, Indian J. Pure Appl. Math 16(7),(1985), 775-790.
Search in Google Scholar Back to article
[5] M. K. Aouf, Bounded spiral-like functions with fixed second coefficients Inter.J.Math.Math. Sci. 12(1), (1989), 113-118.10.1155/S0161171289000153
Search in Google Scholar Back to article
[6] M. K. Aouf, On a new criteria for univalent functions of order α, Rend.Math.Series-II, (1991), 47-59.
Search in Google Scholar Back to article
[7] M. K. Aouf, Subordination properties for a certain class of analytic functions defined by the Salagean operator, Appl. Math. Lett. 22(10),(2009), 1581-1585.10.1016/j.aml.2009.05.005
Search in Google Scholar Back to article
[8] M. K. Aouf, Bounded p-valent Robertson functions defined by using a differential operator, J. Frankl. Inst. 347(10),(2010), 1927-1941.10.1016/j.jfranklin.2010.10.012
Search in Google Scholar Back to article
[9] M. K. Aouf and H.E. Darwish, On inequalities for certain analytic functions involving Ruscheweyh derivative, J. Math., 21(4),(1995), 387-393.
Search in Google Scholar Back to article
[10] M. K. Aouf, H.E. Darwish and A.A.Attiya, A remark on certain regular functions defined by Ruscheweyh derivative, Proc.Pakistan.Acad.Sci., 37(1)(2000),67-69.
Search in Google Scholar Back to article
[11] M. K. Aouf, and A.A.Al-Dohiman, Fixed second coefficient for certain subclasses of starlike functions with negative coefficients, Demonstratio Math., 38(3),(2005),551-565.10.1515/dema-2005-0305
Search in Google Scholar Back to article
[12] M. K. Aouf and H.M.Hossen, Notes on certain classes of analytic function defined by Ruscheweyh derivative, Taiwense.T .Math., 1(1), (1997),11-19.
Search in Google Scholar Back to article
[13] M. K. Aouf and A. O. Mostafa, Some Subordination results for classes of analytic functions defined by the Al-Aboudi operator, Arch. Math., 92(2009), 279-286.10.1007/s00013-009-2984-x
Search in Google Scholar Back to article
[14] M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Subordination results for certain class of analytic functions defined by convolution, Rend. del Circols Mat.di Palermo, no 60,(2011), 255-262.10.1007/s12215-011-0048-0
Search in Google Scholar Back to article
[15] M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Subordination theorem of analytic functions defined by convolution, Complex Anal. Operator Theory, 7,(2013), 1117-1126.10.1007/s11785-011-0171-0
Search in Google Scholar Back to article
[16] A. Aral, V. Gupta and R. P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, 2013.10.1007/978-1-4614-6946-9
Search in Google Scholar Back to article
[17] A.A. Attiya, On some application of a subordination theorems, J. Math. Anal. Appl. 311 (2005), 489-494.10.1016/j.jmaa.2005.02.056
Search in Google Scholar Back to article
[18] T. Bulboacã, Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
Search in Google Scholar Back to article
[19] R.A. El-Ashwah, M. K. Aouf and A.A. Hassan, Subordination results for new subclasses of analytic univalent functions, Thai. J. Math., 15(1),(2017),113-140.
Search in Google Scholar Back to article
[20] B.A, Frasin, Subordination results for a class of analytic functions defined by a linear operator, J. Inequal. Pure Appl. Math. 7: (2006), 1-7.
Search in Google Scholar Back to article
[21] B. A. Frasin and G. Murugusundaramoorthy, A subordination results for a class of analytic functions defined by q-differential operator, Ann. Univ. Paedagog. Crac. Stud. Math. 19 (2020), 53-64.
Search in Google Scholar Back to article
[22] G. Gasper and M. Rahman, Basic Hypergeometric series, Cambridge Univ.Press, New York,1990.
Search in Google Scholar Back to article
[23] F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46(1908), 253–281.10.1017/S0080456800002751
Search in Google Scholar Back to article
[24] S. Kanas and D. Răducanu, Some subclass of analytic functions related to conic domains, Math. Slovaca 64(2014), no. 5, 1183–1196.
Search in Google Scholar Back to article
[25] P. K. Kulshrestha, Bounded Robertson, Rend.Math., 6 (9) (1976), 137–150.
Search in Google Scholar Back to article
[26] V. Kumar, S.L.Shukla and A.M. Chaudhary, On a class of certain analytic functions of complex order, Tamkang J.Math.,21(2),(1990), 1-9.10.5556/j.tkjm.21.1990.4643
Search in Google Scholar Back to article
[27] J. E. Littlewood, On inequalities in theory of functions, Proc. London Math. Soc. 23(1925), 481–519.10.1112/plms/s2-23.1.481
Search in Google Scholar Back to article
[28] S. S. Miller and P. T. Mocanu, Differential subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Dekker, New York, 2000.10.1201/9781482289817
Search in Google Scholar Back to article
[29] M. A. Nasr and M. K. Aouf, On convex functions of complex order, Mansoura Bull. Sci., 8 (1982), 565-582.
Search in Google Scholar Back to article
[30] M. A. Nasr and M. K. Aouf, Bounded starlike functions of complex order, Proc. Indian Acad.Sci.,Math.,92 (1983), 97-102.10.1007/BF02863012
Search in Google Scholar Back to article
[31] M. A. Nasr and M. K. Aouf, Starlike function of complex order, J. Natur. Sci. Math., 25 (1985),1-12.
Search in Google Scholar Back to article
[32] S.Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.10.1090/S0002-9939-1975-0367176-1
Search in Google Scholar Back to article
[33] T. M. Seoudy and M. K. Aouf, Convolution properties for certain classes of analytic functions defined by q-derivative operator, Abstr. Appl. Anal., Vol. 2014, no. Article ID 846719, pp. 1-7, 2014, doi: 10.1155/2014/846719.10.1155/2014/846719
Search in Google Scholar Back to article
[34] T. M. Seoudy and M. K. Aouf, Coefficient estimates of new class of q-starlike and q-convex functions of complex order. J. Math. Inequal., 10,(2016), 135-145.10.7153/jmi-10-11
Search in Google Scholar Back to article
[35] H. Silverman. Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51(1975),109–116.10.1090/S0002-9939-1975-0369678-0
Search in Google Scholar Back to article
[36] H. Silverman, A survey with open problems on univalent functions whose coefficients are negative. Rocky Mt. J.Math. 21(1991),1099–1125.
Search in Google Scholar Back to article
[37] H. Silverman, Integral means for univalent functions with negative coefficients, Houston J. Math. 23(1997),169–174.
Search in Google Scholar Back to article
[38] S. Singh, A subordination theorems for spirallike functions, IJMMS, 24(7) (2000), 433–435.10.1155/S0161171200004634
Search in Google Scholar Back to article
[39] R. Singh and V.Singh, On a class of bounded starlike functions, Indian J. Pure Appl. Math.,5,(1974),733–740.
Search in Google Scholar Back to article
[40] H.M. Srivastava and A.A. Attiya, Some subordination results associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math., 5(4) (2004), Article 82, 1–6.
Search in Google Scholar Back to article
[41] H.S. Wilf, Subordinating factor sequence for convex maps of the unit circle, Proc. Amer. Math. Soc. 12 (1961), 689–693.10.1090/S0002-9939-1961-0125214-5
Search in Google Scholar Back to article

Subordination results for a class of analytic functions

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