On Special Fuzzy Differential Subordinations Using Generalized Sala gean Operator and Ruscheweyh Derivative

## Keywords

Fuzzy differential subordination
convex function
fuzzy best dominant
differential operator
Ruscheweyh derivative
generalized Salagean operator

## How to Cite

Alina Alb Lupas. (2017). On Special Fuzzy Differential Subordinations Using Generalized Sala gean Operator and Ruscheweyh Derivative. Journal of Advances in Applied & Computational Mathematics, 4(1), 26–34. https://doi.org/10.15377/2409-5761.2017.04.5

## Abstract

: In the present paper we establish several fuzzy differential subordinations regardind the operator RD!,"
m , given
by RD!,"
m : A # A, RD!,"
m f (z) = (1#")Rm f (z)+"D!
m f (z), where Rm f (z) denote the Ruscheweyh derivative, D!
m f (z) is the
generalized S !
a l
!
a gean operator and A = { f !H(U), f (z) = z + a2z
2 +…, z !U} is the class of normalized analytic
functions. A certain fuzzy class, denoted by RDm
F (!,",# ), of analytic functions in the open unit disc is introduced by
means of this operator. By making use of the concept of fuzzy differential subordination we will derive various properties and characteristics of the class RDm
F (!,",# ). Also, several fuzzy differential subordinations are established regarding
the operator RD!,"
m .

## References

Alb Lupas A. On special differential subordinations using Salagean and Ruscheweyh operators, Mathematical Inequalities and Applications 2009; 12(4): 781-790. https://doi.org/10.7153/mia-12-61

Alina Alb Lupas. On a certain subclass of analytic functions defined by Salagean and Ruscheweyh operators, Journal of Mathematics and Applications 2009; 31: 67-76.

Alina Alb Lupas. On special differential subordinations using a generalized Salagean operator and Ruscheweyh derivative, Journal of Computational Analysis and Applications 2011; 13(1): 98-107.

Alb Lupas A. On a certain subclass of analytic functions defined by a generalized Salagean operator and Ruscheweyh derivative, Carpathian Journal of Mathematics 2012; 28(2): 183-190.

Alb Lupas A. Daniel Breaz, On special differential superordinations using Salagean and Ruscheweyh operators, Geometric Function Theory and Applications’ 2010 (Proc. of International Symposium, Sofia 2010; 27-31: 98-103.

Alb Lupas A. On special differential superordinations using a generalized Salagean operator and Ruscheweyh derivative, Computers and Mathematics with Applications 2011; 61: 1048-1058. https://doi.org/10.1016/j.camwa.2010.12.055

Alina Alb Lupas. Certain special differential superordinations using a generalized Salagean operator and Ruscheweyh derivative, Analele Universitatii Oradea, Fasc. Matematica, Tom 2011; XVIII: 167-178.

Alb Lupas A. Gh. Oros, On special fuzzy differential subordinations using Salagean and Ruscheweyh operators, submitted Applied Mathematics and Computation.

Alina Alb Lupas. A Note on Special Fuzzy Differential Subordinations Using Generalized Salagean Operator and Ruscheweyh Derivative, Journal of Computational Analysis and Applications 2013; 15(8): 1476-1483.

Al-Oboudi FM. On univalent functions defined by a generalized Salagean operator. Ind J Math Math Sci 2004; 27: 1429-1436. https://doi.org/10.1155/S0161171204108090

Gh. Gal S, Ban AI. Elemente de matematic a fuzzy, Oradea, 1996.

Miller SS and Mocanu PT. Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978), 298-305. https://doi.org/10.1016/0022-247X(78)90181-6

Miller SS and Mocanu PT. Differential subordinations and univalent functions, Michigan Math J 1985; 32: 157-171.

Miller SS and Mocanu PT. Differential Subordinations. Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics Marcel Dekker Inc., New York, Basel 2000; 225.

Oros GI and Oros Gh. The notion of subordination in fuzzy sets theory, General Mathematics 2011; 19(4): 97-103.

Oros GI and Oros Gh. Fuzzy differential subordinations, Acta Universitatis Apulensis 2012; 30: 55-64.

Oros GI and Oros Gh. Dominant and best dominant for fuzzy differential subordinations, Stud. Univ. Babes-Bolyai Math 2012; 57(2): 239-248.

Ruscheweyh St. New criteria for univalent functions. Proc Amet Math Soc 1975; 49: 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1

Salagean GSt. Subclasses of univalent functions, Lecture Notes in Math. Springer Verlag Berlin 1983; 1013: 362-372.