Univalent Functions Formulated by the Salagean-Difference Operator

Ibrahim, Rabha W.; Darus, Maslina

doi:10.28924/2291-8639-17-2019-652

Research Article

Univalent Functions Formulated by the Salagean-Difference Operator

Rabha W. Ibrahim¹*
Maslina Darus

* Corresponding author

Abstract

We present a class of univalent functions Tm(κ, α) formulated by a new differential-difference operator in the open unit disk. The operator is a generalization of the well known Salagean's differential operator. Based on this operator, we define a generalized class of bounded turning functions. Inequalities, extreme points of Tm(κ, α), some convolution properties of functions fitting to Tm(κ, α), and other properties are discussed.

How to Cite

R. W. Ibrahim, M. Darus, Univalent Functions Formulated by the Salagean-Difference Operator, Int. J. Anal. Appl. 17 (2019), 652–658. https://doi.org/10.28924/2291-8639-17-2019-652

BibTeX

@article{Ibrahim2019,
  author  = {Ibrahim, Rabha W. and Darus, Maslina},
  title   = {Univalent Functions Formulated by the Salagean-Difference Operator},
  journal = {Int. J. Anal. Appl.},
  volume  = {17},
  year    = {2019},
  pages   = {652--658},
  doi     = {10.28924/2291-8639-17-2019-652}
}

References

[1] G.S. Salagean, Subclasses of univalent functions, Complex Analysis-Fifth Romanian-Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., vol. 1013, Springer, Berlin, (1983), 362-372.
[2] C.F. Dunkl, Differential-difference operators associated with reflections groups, Trans. Amer. Math. Soc. 311 (1989), 167- 183.
[3] R. W. Ibrahim, New classes of analytic functions determined by a modified differential-difference operator in a complex domain, Karbala Int. J. Modern Sci. 3(1) (2017), 53-58.
[4] J.M. Jahangiri, K. Farahmand, Partial sums of functions of bounded turning, J. Inequal. Pure Appl. Math. 4(4) (2003), Article 79.
[5] M. Darus M, R.W Ibrahim, Partial sums of analytic functions of bounded turning with applications, Comput. Appl. Math. 29 (1) 2010), 81-88.
[6] R.W Ibrahim, M. Darus, Extremal bounds for functions of bounded turning, Int. Math. Forum. 6 (33) (2011), 1623-1630.
[7] R.W Ibrahim, Upper bound for functions of bounded turning. Math. Commun. 17(2) (2012), 461-468.
[8] S.S. Miller, and P. T. Mocanu. Differential subordinations: theory and applications. CRC Press, 2000.
[9] R.W Ibrahim, Optimality and duality defined by the concept of tempered fractional univex functions in multi-objective optimization. Int. J. Anal. Appl. 15 (1) (2017), 75-85.