Certain subclass of analytic functions defined by q-analogue generalized differential operator

S. Sridevi; b venkateswarlu; Sujatha

doi:10.5269/bspm.78615

S. Sridevi Department of Mathematics, GSS, GITAM University, Doddaballapur- 562 163, Bengaluru North, Karnataka, India.
b venkateswarlu
Sujatha Department of Mathematics, GSS, GITAM University, Doddaballapur- 562 163, Bengaluru North, Karnataka, India.

Resumo

In the present work, we define a subclass of uniformly starlike functions corresponding to the class of uniformly convex functions involving the q-analogue of a generalized differential operator. Furthermore, we discuss coefficient estimates, neighborhoods, partial sums, integral means inequality, and Radii of close-to-convexity and Starlikeness results related to the defined class.

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Referências

Ahuja, O. P., Murugusundaramoorthy, G., and Magesh, N., Integral means for uniformly convex and starlike functions associated with generalized hypergeometric functions, J. Inequal. Pure Appl. Math. 8(4), Article 118, 9 pp, (2007).

Al-Oboudi, F. M., On univalent functions defined by a generalized S˘al˘agean operator, Int. J. Math. Sci. 27, 1429–1436, (2004).

Aqlan, E., Jahangiri, J. M., and Kulkarni, S. R., New classes of k-uniformly convex and starlike functions, Tamkang J. Math. 35(3), 261-266, (2004).

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

Goodman, A. W., On uniformly starlike functions, J. Math. Anal. Appl. 155(2), 364-370, (1991).

Govindaraj, M., and Sivasubramanian, S., On a class of analytic functions related to conic domains involving q-calculus, Anal. Math. 43(3), 475-487, (2017).

Jackson, F. H., q-Difference Equations, Amer. J. Math. 32(4), 305-314, (1910).

Littlewood, J. E., On Inequalities in the Theory of Functions, Proc. London Math. Soc. 23(7), 481-519, (1925).

Magesh, N., Altınkaya., and Yalcın, S., Certain subclasses of k-uniformly starlike functions associated with symmetric q-derivative operator, J. Comput. Anal. Appl. 24(8), 1464-1473, (2018).

Owa, S., Sekine, T., and Yamakawa, R., On Sakaguchi type functions, Appl. Math. Comput. 187(1), 356-361, (2007).

Reddy, P.T., and Venkateswarlu, B., A certain subclass of uniformly convex functions defined by Bessel functions, Proyecciones. 38(4), 719-731, (2019).

Ruscheweyh, S., Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81(4), 521-527, (1981).

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

Sakaguchi, K. B., On a certain univalent mapping, J. Math. Soc. Japan. 11, 72-75, (1959).

Salagean, G., Subclasses of univalent functions, in Complex analysis—fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math. Springer, Berlin. 1013, 362-372, (1981).

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

Silverman, H., Partial sums of starlike and convex functions, J. Math. Anal. Appl. 1, 221-227, (1997).

Silverman, H., Integral means for univalent functions with negative coefficients, Houston J. Math. 23(1), 169-174, (1997).