Research Article

Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator

Number: 31 June 30, 2020
Nasir Khan *, Bakhtiar Ahmad , Bilal Khan , Muhammad Nisar
EN

Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator

Abstract

In this paper, we consider some new subclasses of analytic functions with bounded boundary and bounded radius rotation associated with Attia-Srivastava operator. The coefficient bounds, integral representations, convolution properties belong to theses classes are investigated.                                                                                                                 

                                                                                                                                                               

Keywords

Srivastava-Attia operator, Janowski fuctions, subordination, convolution, starlike convex functions

References

  1. A. Aral, V. Gupta, On q-Baskakov Type Operators, Demonstratio Mathematica 1(42) (2009) 109-122.
  2. T. Bulboaca, Differential Subordinations and Superordinations, Recent Results, House of Scientic Book Publ. Cluj-Napoca, 2005.
  3. S. S. Miller, P. T. Mocanu, Subordinates of Differential Superordinations, Complex Variables 48(10) (2003) 815-826.
  4. Y. Polatoglu, M. Bolcal, A. Sen, E. Yavuz, A Study on The Generalization of Janowski Functions in The Unit Disc, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis 22 (2006) 27-31.
  5. W. Janowski, Some Extremal Problems for Certain Families of Analytic Functions, Annales Polonici Mathematici 28 (1973) 297-326.
  6. N. Khan, B. Khan, Q. Z. Ahmad, S. Ahmad, Some Convolution Properties of Multivalent Analytic Functions, AIMS Mathematics 2(2) (2017) 260-268.
  7. S. Mahmood, H. M. Srivastava, N. Khan, Q. Z. Ahmad, B. Khan, I. Ali, Upper Bound of The Third Hankel Determinant for a Subclass of q-Starlike Functions, Symmetry 11 (2019) Article ID 347 1-13.
  8. S. Mahmood, Q. Z. Ahmad, H. M. Srivastava, N. Khan, B. Khan, M. Tahir, A Certain Subclass of Meromorphically q-Starlike Functions Associated with The Janowski Functions, Journal of Inequalities and Applications 2019 (2019) Article ID 88 1-11.
  9. K. I. Noor, N. Khan, M. Darus, Q. Z. Ahmad, B. Khan, Some Properties of Analytic Functions Associated with Conic Type Regions, International Journal of Analysis and Applications 16(5) (2018) 689-701.
  10. K. I. Noor, N. Khan, K. Piejko, Alpha Convex Functions Associated with Conic Domain, Inter- national Journal of Analysis and Applications 11(2) (2016) 70-80.
APA
Khan, N., Ahmad, B., Khan, B., & Nisar, M. (2020). Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator. Journal of New Theory, 31, 20-31. https://izlik.org/JA97NA99US
AMA
1.Khan N, Ahmad B, Khan B, Nisar M. Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator. JNT. 2020;(31):20-31. https://izlik.org/JA97NA99US
Chicago
Khan, Nasir, Bakhtiar Ahmad, Bilal Khan, and Muhammad Nisar. 2020. “Some Variations of Janowski Functions Associated With Srivastava-Attiya Operator”. Journal of New Theory, nos. 31: 20-31. https://izlik.org/JA97NA99US.
EndNote
Khan N, Ahmad B, Khan B, Nisar M (June 1, 2020) Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator. Journal of New Theory 31 20–31.
IEEE
[1]N. Khan, B. Ahmad, B. Khan, and M. Nisar, “Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator”, JNT, no. 31, pp. 20–31, June 2020, [Online]. Available: https://izlik.org/JA97NA99US
ISNAD
Khan, Nasir - Ahmad, Bakhtiar - Khan, Bilal - Nisar, Muhammad. “Some Variations of Janowski Functions Associated With Srivastava-Attiya Operator”. Journal of New Theory. 31 (June 1, 2020): 20-31. https://izlik.org/JA97NA99US.
JAMA
1.Khan N, Ahmad B, Khan B, Nisar M. Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator. JNT. 2020;:20–31.
MLA
Khan, Nasir, et al. “Some Variations of Janowski Functions Associated With Srivastava-Attiya Operator”. Journal of New Theory, no. 31, June 2020, pp. 20-31, https://izlik.org/JA97NA99US.
Vancouver
1.Nasir Khan, Bakhtiar Ahmad, Bilal Khan, Muhammad Nisar. Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator. JNT [Internet]. 2020 Jun. 1;(31):20-31. Available from: https://izlik.org/JA97NA99US