This paper aims to present a survey on certain fuzzy subordination properties for analytic functions defined in the open unit disk. The new results are derived by considering a certain differential operator. By making use of two differential properties of the operator we determine sufficient conditions to find the fuzzy best dominants for several fuzzy differential subordinations. Some interesting further fuzzy consequences are also considered.
Al-Oboudi FM. On univalent functions defined by a generalized S l gean operator. Int J Math Math Sci. 2004; 27: 1429-1436. https://doi.org/10.1155/S0161171204108090
Al-Shaqsi K, Darus M. On univalent functions with respect to k-symmetric points defined by a generalized Ruscheweyh derivatives operator. Journal of Analysis and Applications, 2009; 7(1): https://doi.org/10.1155/2008/259205
Altınkaya S, Wanas AK. Some properties for fuzzy differential subordination defined by Wanas operator. Earthline J Math Sci. 2020; 4: 51-62. https://doi.org/10.34198/ejms.4120.5162
Cătaş A. On certain class of -valent functions defined by a new multiplier transformations. Proceedings Book of the International Symposium G.F.T.A., Istanbul Kultur University, Turkey, 2007; 241-250.
Cătaş A, Borșa E, Iambor L. Best dominants and subordinants for certain sandwich-type theorems. Symmetry 2022; 14(1): 62-Special issue: Symmetry in Functional Equations and Analytic Inequalities II. https://doi.org/10.3390/sym14010062
Cho NE, Srivastava HM. Argument estimates of certain analytic functions defined by a class of multiplier transformations. Math Comput Modelling, 2003; 37(1-2): 39-49. https://doi.org/10.1016/S0895-7177(03)80004-3
Cho NE, Kim TH. Multiplier transformations and strongly close-to-convex functions. Bull Korean Math Soc. 2003; 40(3): 399-410. https://doi.org/10.4134/BKMS.2003.40.3.399
Cotrla LI, Cătaş A. Differential sandwich theorem for certain class of analytic functions associated with an integral operator. Studia Universitatis Babes-Bolyai, Mathematica, 2020; 65(4): 487-494. https://doi.org/10.24193/subbmath.2020.4.01
Darus M, Al-Shaqsi K. Differential sandwich theorems with generalized derivative operator. Int J Comput Math Sci. 2008; 2(2): 75-78. https://doi.org/10.5772/8210
El-Deeb SM, Alb Lupas A. Fuzzy differential subordinations associated with an integral operator. An Univ Oradea Fasc Mat 2020; XXVII: 133-140.
El-Deeb SM, Oros GI. Fuzzy differential subordinations connected with the linear operator. Math Bohem. 2021; 1-10. https://doi.org/10.21136/MB.2020.0159-19
Alb Lupas A, Cătaş, A. Fuzzy Differential Subordination of the Atangana-Baleanu Fractional Integral, Symmetry, 2021; 13(10): 1929. https://doi.org/10.3390/sym13101929.
Alb Lupas A. Oros GI. New Applications of S l gean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations. Mathematics, 2021; 9: 2000. https://doi.org/10.3390/math9162000
Miller SS, Mocanu PT. Differential Subordinations: Theory and Applications. Pure and Applied Mathematics, No. 225, Marcel Dekker, New York, 2000. https://doi.org/10.1201/9781482289817
Ruscheweyh S. New criteria for univalent functions. Proc Amer Math Soc. 1975; 49: 109-115, https://doi.org/10.1090/S0002-9939-1975-0367176-1
Srivastava HM, El-Deeb SM. Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution. Symmetry, 2021; 13: 1023. https://doi.org/10.3390/sym13061023
Salagean GS. Subclasses of Univalent functions. Lecture Note Math. 1983; 1013: 362-372. https://doi.org/10.1007/BFb0066543
Oros GI, Oros Gh. The notion of subordination in fuzzy sets theory. General Mathematics, 2011; 19: 97-103.
Oros GI, Oros Gh. Fuzzy differential subordination. Acta Universitatis Apulensis, 2012; 30: 55-64.
Oros GI, Oros Gh. Dominants and best dominants in fuzzy differential subordinations. Stud Univ Babes - Bolyai Math. 2012; 57: 239-248.
Oros GI. New fuzzy differential subordinations. Commun Fac Sci Univ Ank Ser A1 Math Stat. 2021; 70: 229-240. https://doi.org/10.31801/cfsuasmas.784080
Wanas AK, Hussein DA. Fuzzy Differential Subordinations Results for l-pseudo Starlike and l-pseudo Convex Functions with Respect to Symmetrical Points. Earthline J Math Sci. 2020; 4: 129-137. https://doi.org/10.34198/ejms.4120.129137
Zadeh LA. Fuzzy sets. Inform Control, 1965; 8: 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
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