FUZZY DIFFERENTIAL SUBORDINATION INVOLVING GENERALIZED NOOR-RUSCHEWEYH OPERATOR
Abstract
A new operator Lnλ is introduced as a convex combination of Ruscheweyh derivative operator and Noor integral operator on the class A of analytic functions in the open unit disc E. The operator Lnλ is studied using fuzzy set theory and fuzzy differential subordination. All the results proved are sharp. Some interesting special cases are derived as corollaries for particular choices of the functions acting as fuzzy best dominant.
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A. Alb Lupas and G. Oros: On special fuzzy differential subordinations using Salagean and Ruscheweyh operators, Appl. Math. Comput., 261(2015), 119-127.
W. G. Atshan and K. O. Hussain: Fuzzy differential subordination, Theory Appl. Math.Comput. Sci. 7(1)(2017), 27-38.
J. L. Liu and K. I. Noor: On subordinationsfor certain analytic functions associaated with Noor integral operator, Appl. Math. Comput. 137 (2007), 1453- 1460.
S. S. Miller and P. T. Mocanu: Differential subordinattion and univalent functions, Michig. Math. J. 28(1981), 157-171
S. S. Miller and P. T. Mocanu: Differential Subordination: Theory and Applications, Monograh Text Books, Pure Appl. Math. Vol. 225, Marcel Dekker, New York, 2000.
K. I. Noor and M. A. Noor: Some applications of fuzzy subordinations, J. Advanc. Math. Stud., 15(2022).
K. I. Noor and M. A. Noor: Fuzzy subordinations involving Noor-Salagean operator, Inform. Sci. Letters, 11(6)(2022), 1905-1911.
K. I. Noor and M. A. Noor: On integral operators, J. Math. Anal. Appl. 238(1)(1999), 341-352.
K. I. Noor and M. A. Noor: On certain classes of analytic functions defined by Noor integral operaor, J. Math. Anal. Appl. 281(1) (2003), 244-250.
G. I. Oros and G. Oros: The notion of subordination in fuzzy sets theory, General Math., 19(2011), 97-103.
G. I. Oros and G. Oros: Dominants and best dominants in fuzzy differential subordinations, Stud. Univ. Babes-Bdlyai. Math. 57(2012), 239-248.
G. I. Oros and G. Oros: Fuzzy differential subordination, Acta Universtatics Aplulensis, 30(2012), 55-64.
G. I. Oros and G. Oros: Fuzzy differential subordinations obtained using a hypergeometric integral operator, Mathematics, 9(2021): ID-2539.
S. Ruscheweyh: New Criteria for univalent functions, Proceed. Amer. Math. Soc., 49(1)(1975), 109-115.
I. A. Zadeh: Fuzzy sets, Inform. Control, 8(1965), 335-353.
DOI: https://doi.org/10.22190/FUMI220312026N
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