A subordination results for a class of analytic functions defined by q-differential operator

Basem Frasin, Gangadharan Murugusundaramoorthy

Abstract


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

Keywords


Analytic functions, Univalent functions; Subordinating factor sequence; q-difference operator; Hadamard product (or convolution)

Mathematics Subject Classification (2010)


30C45

References


Aouf, Mohamed Kamal et al. "beta-uniformly convex and starlike functions." Proc. Pakistan Acad. Sci. 46, no. 2 (2009): 97-101.

Araci, Serkan et al. "A certain (p, q)-derivative operator and associated divided differences." J. Inequal. Appl. 2019 (2019): Paper No. 301.

Aral, Ali, Vijay Gupta, and Ravi P. Agarwal. Applications of q-calculus in operator theory. New York: Springer, 2013.

Attiya, Adel A. "On some applications of a subordination theorem." J. Math. Anal. Appl. 311, no. 2 (2005): 489-494.

Al-Oboudi, Fatima M. "On univalent functions defined by a generalized Salagean operator." Int. J. Math. Math. Sci. no. 25-28 (2004): 1429-1436.

Frasin, Basem Aref. "Subordination results for a class of analytic functions defined by a linear operator." JIPAM. J. Inequal. Pure Appl. Math. 7 (2006): Article 4.

Jackson, Frederick H., "On q-functions and a certain difference operator." Trans. Royal Soc. Edinb. 46 (1908): 253-281.

Gangadharan, A., Tirunelveli Nellaiappan Shanmugam, and Hari Mohan Srivastava. "Generalized hypergeometric functions associated with k-uniformly convex functions." Comput. Math. Appl. 44, no. 12 (2002): 1515-1526.

Goodman, Adolph W. "On uniformly convex functions." Ann. Polon. Math. 56, no. 1 (1991): 87-92.

Goodman, Adolph W. "On uniformly starlike functions." J. Math. Anal. Appl. 155, no. 2 (1991): 364-370.

Govindaraj, M., and Srikandan Sivasubramanian. "On a class of analytic functions related to conic domains involving q-calculus." Anal. Math. 43, no. 3 (2017): 475-487.

Kanas, Stanisława R. and Dorina Raducanu. "Some class of analytic functions related to conic domains." Math. Slovaca 64, no. 5 (2014): 1183-1196.

Kanas, Stanisława R., and Agnieszka Wisniowska. "Conic regions and k-uniform convexity." J. Comput. Appl. Math. 105, no. 1-2 (1999): 327-336.

Kanas, Stanisława R., and Agnieszka Wisniowska. "Conic domains and starlike functions." Rev. Roumaine Math. Pures Appl. 45, no. 4 (2000): 647-657.

Kanas, Stanisława R., and Hari Mohan Srivastava. "Linear operators associated with k-uniformly convex functions." Integral Transform. Spec. Funct. 9, no. 2 (2000): 121-132.

Karahuseyin, Zeliha, Sahsene Altinkaya, and Sibel Yalçin. "On H3(1) Hankel determinant for univalent functions defined by using q−derivative operator." TJMM 9, no. 1 (2017): 25-33.

Littlewood, John Edensor. "On Inequalities in the Theory of Functions." Proc. London Math. Soc. 23, no. 7 (2): 481-519.

Ma, Wan Cang, and David Minda. "Uniformly convex functions." Ann. Polon. Math. 57, no. 2 (1992): 165-175.

Rønning, Frode. "Uniformly convex functions and a corresponding class of starlike functions." Proc. Amer. Math. Soc. 118, no. 1 (1993): 189-196.

Rønning, Frode. "On starlike functions associated with parabolic regions." Ann. Univ. Mariae Curie-Skłodowska Sect. A 45, no. 1991 (1992): 117-122.

Salagean, Grigore Stefan. "Subclasses of univalent functions." Complex Analysis: Fifth Romanian- Finnish Seminar, Part I(Bucharest, 1981) Vol. 1013 of Lecture Notes in Mathematics, 362-372. Berlin, New York: Springer-Verlag, 1983.

Silverman, Herb. "Univalent functions with negative coefficients." Proc. Amer. Math. Soc. 51 (1975): 109-116.

Silverman, Herb. "A survey with open problems on univalent functions whose coefficients are negative." Rocky Mountain J. Math. 21, no. 3 (1991): 1099-1125.

Silverman, Herb. "Integral means for univalent functions with negative coefficients." Houston J. Math. 23, no. 1 (1997): 169-174.

Singh, Sukhjit. "A subordination theorem for spirallike functions." Int. J. Math. Math. Sci. 24, no. 7 (2000): 433-435.

Srivastava, Hari Mohan. "Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials." Appl. Math. Inf. Sci. 5, no. 3 (2011): 390-444.

Srivastava, Hari Mohan, and Adel A. Attiya. "Some subordination results associated with certain subclasses of analytic functions." JIPAM. J. Inequal. Pure Appl. Math. 5, no. 4 (2004): 6pp.

Wilf, Herbert Saul. "Subordinating factor sequences for convex maps of the unitcircle." Proc. Amer. Math. Soc. 12 (1961): 689-693.


Full Text: PDF

Download statistics: 685

Licencja Creative Commons
This article by Basem Frasin, Gangadharan Murugusundaramoorthy is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej