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Keywords:
analytic function; coefficient estimates; Hadamard product; Hilbert space operator
analytic function; coefficient estimates; Hadamard product; Hilbert space operator
Summary:
Using a Hilbert space operator, we define a new subclass of analytic functions defined by $p$-valent $q$-Sălăgean operator and determine coefficient estimates, distortion bounds, radii of close-to-convexity, starlikeness, and convexity for the functions in this class. We also investigate extreme points and the modified Hadamard product.
References:
[1] Dunford, N., Schwartz, J. T.: Linear Operators. I. General Theory. Pure and Applied Mathematics 7. Interscience Publishers, New York (1958). MR 0117523 | Zbl 0084.10402
[2] El-Qadeem, A. H., Mamon, M. A.: Comprehensive subclasses of multivalent functions with negative coefficients defined by using a $q$-difference operator. Trans. A. Razmadze Math. Inst. 172 (2018), 510-526. DOI 10.1016/j.trmi.2018.04.002 | MR 3907641 | Zbl 1421.30019
[3] Fan, K.: Analytic functions of a proper contraction. Math. Z. 160 (1978), 275-290. DOI 10.1007/BF01237041 | MR 0482310 | Zbl 0455.47013
[4] Ghanim, F., Darus, M.: On new subclass of analytic $p$-valent function with negative coefficient for operator on Hilbert space. Int. Math. Forum 3 (2008), 69-77. MR 2373487 | Zbl 1159.30311
[5] Jackson, F. H.: On $q$-functions and a certain difference operator. Trans. Royal Soc. Edinburgh 46 (1909), 253-281. DOI 10.1017/S0080456800002751
[6] Jackson, F. H.: On $q$-definite integrals. Quar. J. Pure Appl. Math. 41 (1910), 193-203 \99999JFM99999 41.0317.04.
[7] Joshi, S., Joshi, S. B., Mohapatra, R.: On a subclass of analytic functions for operator on a Hilbert space. Stud. Univ. Babeş-Bolyai, Math. 61 (2016), 147-153. MR 3517477 | Zbl 1389.30055
[8] Kim, Y. C., Choi, J. H., Lee, J. S.: Generalized fractional calculus to a subclass of analytic functions for operators on Hilbert space. Int. J. Math. Math. Sci. 21 (1998), 671-676. DOI 10.1155/S0161171298000921 | MR 1642192 | Zbl 0912.30003
[9] Yu, X.: A subclass of analytic $p$-valent functions for operator on Hilbert space. Math. Jap. 40 (1994), 303-308. MR 1297246 | Zbl 0843.30019
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