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

https://izlik.org/JA97NA99US

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

• 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.