Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator
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.
___
- A. Aral, V. Gupta, On q-Baskakov Type Operators, Demonstratio Mathematica 1(42) (2009)
109-122.
- T. Bulboaca, Differential Subordinations and Superordinations, Recent Results, House of Scientic
Book Publ. Cluj-Napoca, 2005.
- S. S. Miller, P. T. Mocanu, Subordinates of Differential Superordinations, Complex Variables
48(10) (2003) 815-826.
- 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.
- W. Janowski, Some Extremal Problems for Certain Families of Analytic Functions, Annales
Polonici Mathematici 28 (1973) 297-326.
- N. Khan, B. Khan, Q. Z. Ahmad, S. Ahmad, Some Convolution Properties of Multivalent Analytic
Functions, AIMS Mathematics 2(2) (2017) 260-268.
- 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.
- 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.
- 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.
- 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.
- K. I. Noor, N. Khan, Some Variations of Janowski Functions Associated with m-Symmetric
Points, Journal of New Theory 11 (2016) 16-28.
- K. I. Noor, N. Khan, Q. Z. Ahmad, N. Khan, Y. L. Chung, On Certain Subclass of Analytic
Functions, Armenian Journal of Mathematics 10(11) (2018) 1-15.
- H. M. Srivastava, Q. Z. Ahmad, N. Khan, N. Khan, B. Khan, Hankel and Toeplitz Determinants
for A Subclass of q-Starlike Functions Associated with A General Conic Domain, Mathematics 7
(2019) Article ID 181 1-15.
- H. M. Srivastava, M. Tahir, B. Khan, Q. Z. Ahmad, N. Khan, Some General Classes of q-Starlike
Functions Associated with The Janowski Functions, Symmetry 11 (2019) Article ID 292 1-14.
- M. Sabil, Q. Z. Ahmad, B. Khan, M. Tahir, N. Khan, Generalisation of Certain Subclasses
of Analytic and bi-univalent Functions, Maejo International Journal of Science and Technology
13(01) (2019) 1-9.
- J. Dziok, Meromorphic Functions with Bounded Boundary Rotation, Acta Mathematica Scientia
34(2) (2014) 466-472.
- B. Pinchuk, Functions of Bounded Boundary Rotation, Israel Journal of Mathematics 10 (1971)
6-16.
- H. M. Srivastava, J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Aca-
demic Publishers, Dordrecht, The Netherlands 2001.
- H. M. Srivastava, A. A. Attiya, An Integral Operator Associated with The Hurwitz-Lerch Zeta
Function and Differential Subordination, Integral Transforms and Special Functions 18 (2007)
207-216.
- J. L. Liu, Subordinations for Certain Multivalent Analytic Functions Associated with The Gener-
alized Srivastava-Attiya Operator, Integral Transforms and Special Functions 19 (2008) 893-901.
- S. D. Lin, H. M. Srivastava, Some families of the Hurwitz-Lerch Zeta functions and associated
fractional derivative and other integral representations, Applied Mathematics and Computation
154 (2004) 725-733.
- D. Raducanu, H. M Srivastava, A New Class of Analytic Functions De ned by means of A Con-
volution Operator Involving The Hurwitz-Lerch Zeta Function, Integral Transforms and Special
Functions 18 (2007) 933-943.
- J. W. Alexander, Functions Which Map The Interior of The Unit Circle upon Simple Regions,
Annals of Mathematics Second Series 17(1) (1915) 12-22.
- S. D. Bernardi, Convex and Starlike Univalent Functions, Transactions of the American Mathe-
matical Society 135 (1969) 429-446.
- K. I. Noor, K. Yousaf, On Classes of Analytic Functions Related with Generalized Janowski
Functions, World Applied Sciences Journal 13 (2011) 40-47.
- K. I. Noor, M. Arif, Mapping Properties of An Integral Operator, Applied Mathematics Letters
25 (2012) 1826-1829.
- V. Paatero, Uber Die Konforme Abbildung Von Gebieten, Deren Rander Vonbeschrankter
Drehung Sind, Annales Academiae Scientiarum Fennicae: Series A. 33(9) (1931) page 77.
- K. S. Padmanabhan, R. Parvatham, Properties of A Class of Functions with Bounded Boundary
Rotation, Annales Polonici Mathematici 31 (1975) 311-323.
- W. Rogosinski, On The Coefficients of Subordinate Functions, Proceedings of the London Math-
ematical Society 48(2) (1943) 48-82.
- S. Ruscheweyh, T. Shiel-small, Hadamard Product of Schlicht Functions and Polya-Schoenberg
Conjecture, Commentarii Mathematici Helvetici 48 (1973) 119-135.
- K. I. Noor, S. N. Malik, M. Arif, M. Raza, On Bounded Boundary and Bounded Radius Rotation
Related with Janowski Function, World Applied Sciences Journal 12 (6) (2011) 895-902.
- A. W. Goodman, Univalent Functions, Vol. I & II, polygonal Publishing House, Washington,
New Jersey, 1983.
- K. I. Noor, Higher-Order Close-to-Convex Functions, Math. Japonica 37(1) (1992) 1-8.
- R. J. Libera, Some Classes of Regular Univalent Functions, Proceedings of the American Math-
ematical Society 16 (1965) 755-758.
- A. E. Livingston, On The Radius Of Univalence Of Certain Analytic Functions, Proceedings of
the American Mathematical Society 17 (1996) 352-357.
- H. Silverman, E. M. Silvia, Subclasses of Starlike Functions Subordinate to Convex Functions,
Canadian Journal of Mathematics 1 (1985) 48-61.
- H. Silverman, E. M. Silvia, D. Telage, Convolution Conditions for Convexity, Starlikeness and
Spiral-Likeness, Mathematische Zeitschrift 162 (1978) 125-130.
- S. Hussain, M. Arif, S. N. Malik, Higher Order Close-to-Convex Functions Associated with Attiya-
Srivastava Operator, Bulletin of the Iranian Mathematical Society 40(4) (2014) 911-920.