CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY q−ANALOGUE GENERALIZED DIFFERENTIAL OPERATOR
CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY q−ANALOGUE GENERALIZED DIFFERENTIAL OPERATOR
Abstract
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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References
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[10] S. Owa, T. Sekine and R. Yamakawa, On Sakaguchi type functions, Appl. Math. Comput. 187 (2007), no. 1,
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[12] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115.
[13] P. Thirupathi Reddy and B. Venkateswarlu, A certain subclass of uniformly convex functions defined by Bessel
functions, Proyecciones 38 (2019), no. 4, 719–731.
[14] K. B. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72–75.
[15] G. S˘al˘agean, Subclasses of univalent functions, in Complex analysis—fifth Romanian-Finnish seminar, Part 1
(Bucharest, 1981), 362–372, Lecture Notes in Math., 1013, Springer, Berlin.
[16] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.
[17] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), no. 1, 221–227.
[18] H. Silverman, Integral means for univalent functions with negative coefficients, Houston J. Math. 23 (1997), no. 1,
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associated with generalized hypergeometric functions, JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 4,
Article 118, 9 pp.
[2] F. M. Al-Oboudi, On univalent functions defined by a generalized S˘al˘agean operator, Int. J. Math. Math. Sci.
2004, no. 25-28, 1429–1436.
[3] E. Aqlan, J. M. Jahangiri and S. R. Kulkarni, New classes of k-uniformly convex and starlike functions, Tamkang
J. Math. 35 (2004), no. 3, 261–266.
[4] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598–601.
[5] A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), no. 2, 364–370.
[6] M. Govindaraj and S. Sivasubramanian, On a class of analytic functions related to conic domains involving
q-calculus, Anal. Math. 43 (2017), no. 3, 475–487.
[7] F. H. Jackson, q-Difference Equations, Amer. J. Math. 32 (1910), no. 4, 305–314.
[8] J. E. Littlewood, On Inequalities in the Theory of Functions, Proc. London Math. Soc. (2) 23 (1925), no. 7,
481–519.
[9] N. Magesh, Altınkaya and S. Yal¸cın, Certain subclasses of k-uniformly starlike functions associated with symmetric
q-derivative operator, J. Comput. Anal. Appl. 24 (2018), no. 8, 1464–1473.
[10] S. Owa, T. Sekine and R. Yamakawa, On Sakaguchi type functions, Appl. Math. Comput. 187 (2007), no. 1,
356–361.
[11] S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521–527.
[12] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115.
[13] P. Thirupathi Reddy and B. Venkateswarlu, A certain subclass of uniformly convex functions defined by Bessel
functions, Proyecciones 38 (2019), no. 4, 719–731.
[14] K. B. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72–75.
[15] G. S˘al˘agean, Subclasses of univalent functions, in Complex analysis—fifth Romanian-Finnish seminar, Part 1
(Bucharest, 1981), 362–372, Lecture Notes in Math., 1013, Springer, Berlin.
[16] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.
[17] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), no. 1, 221–227.
[18] H. Silverman, Integral means for univalent functions with negative coefficients, Houston J. Math. 23 (1997), no. 1,
169–174.
Published
2025-10-07
Section
Mathematics and Computing - Innovations and Applications (ICMSC-2025)
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