Some Inclusion and Radius Problems of Certain Subclasses of Analytic Functions

  • Khalida Inayat Noor COMSATS University, Islamabad, Pakistan
  • Muhammad Kamran COMSATS University Islamabad, Park Road, Islamabad, Pakistan
  • Shujaat Ali Shah COMSATS University Islamabad, Pakistan, and Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Pakistan
Keywords: analytic functions, Janowski functions, conic region, multiplier transformation

Abstract

This article presents the study of certain subclasses of analytic functions defined by using the Hadamard product. We derive certain inclusion results and discuss the applications of multiplier transformation. Several radius problems are also investigated.

References

N. E. Cho and J. A. Kim, Inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation, Comput. Math. Appl. 52 (2006), 323-330. https://doi.org/10.1016/j.camwa.2006.08.022

W. Janowski, Some extremal problems for certain families of analytic functions I, Ann. Polon. Math. 28 (1973), 297-326. https://doi.org/10.4064/ap-28-3-297-326

S. Kanas, Alternative characterization of the class k-UCV and related classes of univalent functions, Serdica Math. J. 25 (1999), 341-350.

S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transforms Spec. Funct. 9 (2000), 121-132. https://doi.org/10.1080/10652460008819249

S. Kanas and W. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), 327-336. https://doi.org/10.1016/S0377-0427(99)00018-7

S. Kanas and W. Wisniowska, Conic domains and k-starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), 647-657.

J.-L. Liu, The Noor integral and strongly starlike functions, J. Math. Anal. Appl. 261 (2001), 441-447. https://doi.org/10.1006/jmaa.2001.7489

J.-L. Liu and K. I. Noor, Some properties of Noor integral operator, J. Nat. Geomet. 21 (2002), 81-90.

S. S. Miller and P. T. Mocanu, Differential subordination. Theory and applications, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker Inc., New York, Basel, 2000. https://doi.org/10.1201/9781482289817

K. I. Noor and S. N Malik, On a subclass of starlike univalent functions, Middle-East J. Sci. Research 7 (2011), 769-777.

K. I. Noor and M. A. Noor, On integral operators, J. Math. Anal. Appl. 238 (1999), 341-352. https://doi.org/10.1006/jmaa.1999.6501

Y. Polatoglu, M. Bolcal, A. Sen and E. Yavuz, A study on the generalization of Janowski functions in the unit disc, Acta Math. Acad. Paedagog. Nyhézi. (N.S.) 22 (2006), 27-31.

M. S. Robertson, On the theory of univalent functions, Ann. Math. 37 (1936), 374-408. https://doi.org/10.2307/1968451

S. Ruscheweyh and T. Sheil-small, Hadamard products of {S}chlicht functions and the Pólya-{S}choenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135. https://doi.org/10.1007/BF02566116

D. Raducanu and H. M. Srivastava, A new class of analytic functions defined by means of convolution operator involving the Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct. 18 (2007), 933-943. https://doi.org/10.1080/10652460701542074

Published
2020-07-26
How to Cite
Noor, K. I., Kamran, M., & Shah, S. A. (2020). Some Inclusion and Radius Problems of Certain Subclasses of Analytic Functions. Earthline Journal of Mathematical Sciences, 5(1), 75-86. https://doi.org/10.34198/ejms.5121.7586
Section
Articles