Fuzzy differential subordinations connected with convolution

Sheza M. El-Deeb, Alina Alb Lupaș


The object of the present paper is to obtain several fuzzy differential subordinations associated with Linear operator \(D_{n,δ,g}^{m}f(z)=z+∑_{j=2}^{∞}[1+(j-1)cⁿ(δ)]^{m}a_{j}b_{j}z^{j}\).  Using the operator \(D_{n,δ,g}^{m}\), we also introduce a class \(H_{n,m,δ}^{F}(η,g)\) of univalent analytic functions for which we give some properties.


fuzzy differential subordination; fuzzy best dominant; linear differential operator; convolution

Full Text:



Alb Lupas, A., On special fuzzy differential subordinations using convolution product of Salagean operator and Ruscheweyh derivative, J. Comput. Anal. Appl., 15(2013), no. 8, 1-6.

Alb Lupas, A., Oros, Gh., On special fuzzy differerential subordinations using Salagean and Ruscheweyh operators, Appl. Math. Comput., 261(2015), 119-127.

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

Bulboaca, T., Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.

El-Deeb, S.M., Maclaurin coefficient estimates for new subclasses of bi-univalent functions connected with a q-analogue of Bessel function, Abstr. Appl. Anal., (2020), Article ID 8368951, 1-7, https://doi.org/10.1155/2020/8368951.

El-Deeb, S.M., Alb Lupas, A., Fuzzy differential subordinations associated with an integral operator, An. Univ. Craiova Ser. Mat. Inform. , 27(2020), no. 1, 133-140.

El-Deeb, S.M., Bulboaca, T., Fekete-Szego inequalities for certain class of analytic functions connected with q-anlogue of Bessel function, J. Egyptian Math. Soc., (2019), 1-11,


El-Deeb, S.M., Bulboaca, T., Differential sandwich-type results for symmetric functions connected with a q-analog integral operator, Mathematics, 7(2019), no. 12, 1-17,


El-Deeb, S.M., Oros, G., Fuzzy differential subordinations connected with the linear operator, Math. Bohem., 146(2021), no. 4, 397-406.

Gal, S.G., Ban, A.I., Elemente de Matematica Fuzzy, Editura Univ. din Oradea, 1996.

Miller, S.S., Mocanu, P.T., Differential Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York and Basel, 2000.

Oros, G.I., Oros, Gh., The notation of subordination in fuzzy sets theory, Gen. Math., 19(2011), no. 4, 97-103.

Oros, G.I., Oros, Gh., Fuzzy differential subordination, Acta Univ. Apulensis, 30(2012), 55-64.

Oros, G.I., Oros, Gh., Dominant and best dominant for fuzzy differential subordinations, Stud. Univ. Babes-Bolyai Math., 57(2012), no. 2, 239-248.

Salagean, G.S., Subclasses of univalent functions, Lecture Notes in Math., 1013, Springer Verlag, Berlin, 1983, 362-372.

Srivastava, H.M., El-Deeb, S.M., A certain class of analytic functions of complex order with a q-analogue of integral operators, Miskolc Math. Notes, 21(2020), no. 1, 417-433.

Yousef, F., Al-Hawary, T., Murugusundaramoorthy, G., Fekete-Szego functional problems for some subclasses of bi-univalent functions defined by Frasin differential operator, Afr. Mat., 30(2019), 495-503, https://doi.org/10.1007/s13370-019-00662-7.

DOI: http://dx.doi.org/10.24193/subbmath.2023.1.11


  • There are currently no refbacks.