Geodesic
Fuzzy differential subordinations connected with the linear operator
Mathematica Bohemica, Tome 146 (2021) no. 4, pp. 397-406
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We obtain several fuzzy differential subordinations by using a linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha }f(z)=z+\sum \limits _{k=2}^{\infty }(1+\gamma ( k-1))^{n}m^{\alpha }(m+k)^{-\alpha }a_{k}z^{k}$. Using the linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha },$ we also introduce a class of univalent analytic functions for which we give some properties.
We obtain several fuzzy differential subordinations by using a linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha }f(z)=z+\sum \limits _{k=2}^{\infty }(1+\gamma ( k-1))^{n}m^{\alpha }(m+k)^{-\alpha }a_{k}z^{k}$. Using the linear operator $\mathcal {I}_{m,\gamma }^{n,\alpha },$ we also introduce a class of univalent analytic functions for which we give some properties.
DOI : 10.21136/MB.2020.0159-19
Classification : 30C45
Keywords: fuzzy differential subordination; fuzzy best dominant; linear operator 
@article{10_21136_MB_2020_0159_19,
     author = {El-Deeb, Sheza M. and Oros, Georgia I.},
     title = {Fuzzy differential subordinations connected with the linear operator},
     journal = {Mathematica Bohemica},
     pages = {397--406},
     year = {2021},
     volume = {146},
     number = {4},
     doi = {10.21136/MB.2020.0159-19},
     mrnumber = {4336546},
     zbl = {07442509},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0159-19/}
}
TY  - JOUR
AU  - El-Deeb, Sheza M.
AU  - Oros, Georgia I.
TI  - Fuzzy differential subordinations connected with the linear operator
JO  - Mathematica Bohemica
PY  - 2021
SP  - 397
EP  - 406
VL  - 146
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0159-19/
DO  - 10.21136/MB.2020.0159-19
LA  - en
ID  - 10_21136_MB_2020_0159_19
ER  - 
%0 Journal Article
%A El-Deeb, Sheza M.
%A Oros, Georgia I.
%T Fuzzy differential subordinations connected with the linear operator
%J Mathematica Bohemica
%D 2021
%P 397-406
%V 146
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0159-19/
%R 10.21136/MB.2020.0159-19
%G en
%F 10_21136_MB_2020_0159_19
El-Deeb, Sheza M.; Oros, Georgia I. Fuzzy differential subordinations connected with the linear operator. Mathematica Bohemica, Tome 146 (2021) no. 4, pp. 397-406. doi: 10.21136/MB.2020.0159-19

[1] Al-Oboudi, F. M.: On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci. 25-27 (2004), 1429-1436. | DOI | MR | JFM

[2] Lupaş, A. Alb: On special fuzzy differerential subordinations using convolution product of Sălăgean operator and Ruscheweyh derivative. J. Comput. Anal. Appl. 15 (2013), 1484-1489. | MR | JFM

[3] Lupaş, A. Alb, Oros, G.: On special fuzzy differerential subordinations using Sălăgean and Ruscheweyh operators. Appl. Math. Comput. 261 (2015), 119-127. | DOI | MR | JFM

[4] Aouf, M. K.: Some inclusion relationships associated with the Komatu integral operator. Math. Comput. Modelling 50 (2009), 1360-1366. | DOI | MR | JFM

[5] Aouf, M. K.: The Komatu integral operator and strongly close-to-convex functions. Bull. Math. Anal. Appl. 3 (2011), 209-219. | MR | JFM

[6] Bernardi, S. D.: Convex and starlike univalent functions. Trans. Am. Math. Soc. 135 (1969), 429-446. | DOI | MR | JFM

[7] Bulboacă, T.: Differential Subordinations and Superordinations: Recent Results. House of Scientic Book Publ., Cluj-Napoca (2005).

[8] Ebadian, A., Najafzadeh, S.: Uniformly starlike and convex univalent functions by using certain integral operators. Acta Univ. Apulensis, Math. Inform. 20 (2009), 17-23. | MR | JFM

[9] El-Ashwah, R. M., Aouf, M. K., El-Deeb, S. M.: Differential subordination for certain subclasses of $p$-valent functions associated with generalized linear operator. J. Math. 2013 (2013), Article ID 692045, 8 pages. | DOI | MR | JFM

[10] Gal, S. G., Ban, A. I.: Elemente de Matematica Fuzzy. University of Oradea, Oradea (1996), Romanian.

[11] Khairnar, S. M., More, M.: On a subclass of multivalent $\beta$-uniformly starlike and convex functions defined by a linear operator. IAENG, Int. J. Appl. Math. 39 (2009), 175-183. | MR | JFM

[12] Komatu, Y.: On analytic prolongation of a family of integral operators. Math., Rev. Anal. Numér. Théor. Approximation, Math. 32(55) (1990), 141-145. | MR | JFM

[13] Miller, S. S., Mocanu, P. T.: Differential Subordination: Theory and Applications. Pure and Applied Mathematics, Marcel Dekker 225. Marcel Dekker, New York (2000). | DOI | MR | JFM

[14] Oros, G. I., Oros, G.: The notation of subordination in fuzzy sets theory. Gen. Math. 19 (2011), 97-103. | MR | JFM

[15] Oros, G. I., Oros, G.: Dominants and best dominants in fuzzy differential subordinations. Stud. Univ. Babeş-Bolyai, Math. 57 (2012), 239-248. | MR | JFM

[16] Oros, G. I., Oros, G.: Fuzzy differential subordination. Acta Univ. Apulensis, Math. Inform. 30 (2012), 55-64. | MR | JFM

[17] Raina, R. K., Bapna, I. B.: On the starlikeness and convexity of a certain integral operator. Southeast Asian Bull. Math. 33 (2009), 101-108. | MR | JFM

[18] Sălăgean, G. S.: Subclasses of univalent functions. Complex Analysis -- Fifth Romanian-Finnish Seminar Lecture Notes in Mathematics 1013. Springer, Berlin (1983), 362-372. | DOI | MR | JFM

Cité par Sources :