Year 2020,
Issue: 31, 20 - 31, 30.06.2020
Nasir Khan
Bakhtiar Ahmad
Bilal Khan
Muhammad Nisar
References
- 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 Dened 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.
Some Variations of Janowski Functions Associated with Srivastava-Attiya Operator
Year 2020,
Issue: 31, 20 - 31, 30.06.2020
Nasir Khan
Bakhtiar Ahmad
Bilal Khan
Muhammad Nisar
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.
References
- 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 Dened 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.