Some Properties of Analytic Functions Associated with Conic Type Regions

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Khalida Inayat Noor, Nazar Khan, Maslina Darus, Qazi Zahoor Ahmad, Bilal Khan, Some Properties of Analytic Functions Associated with Conic Type Regions, Int. J. Anal. Appl., 16 (5) (2018), 689-701.

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Khalida Inayat Noor, Nazar Khan, Maslina Darus, Qazi Zahoor Ahmad, Bilal Khan

Abstract

The main purpose of this investigation is to define new subclasses of analytic functions with respect to symmetrical points. These functions map the open unit disk onto certain conic regions in the right half plane. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier known developments.

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References

  1. N. I. Ahiezer, Elements of theory of elliptic functions, Moscow, 1970.
  2. G. D. Anderson, M. K. Vamanamurthy and M. K. Vourinen, Conformal invariants, inequalities and quasiconformal maps, Wiley-Interscience, 1997.
  3. M. Al-Kaseasbeh and M. Darus, Inclusion and convolution properties of a certain class of analytic functions, Eurasian Math. J. 8 (4) (2017), 11-17.
  4. M. Caglar, H. Ohan and E. Deniz, Majorization for certain subclass of analytic functions involving the generalized Noor integral operator, Filomat, 27 (1) (2013), 143-148.
  5. M. Darus and S. Owa, New subclasses concerning some analytic and univalent functions, Chinese J. Math. (2017), Article ID 4674782, 4 pages.
  6. R. N. Das and P. Singh, Radius of convexity for certain subclass of close-to-convex functions, J. Indian Math Soc. 41 (1977), 363-369.
  7. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
  8. M. R. Goel and B. S. Mehrok, A subclass of univalent functions, Houston J. Math. 8 (1982), 343-357.
  9. W. Janowski, Some extremal problem for certain families of analytic functions I, Ann. Polon. Math. 28 (1973), 298-326.
  10. A. Janteng and S. A. Halim, A subclass of convex functions with respect to symmetric points, Proceedings of The 16th National Symposium on Science Mathematical, 2008.
  11. S. Kanas and A. Wi ´sniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), 327-336.
  12. S. Kanas and A. Wi ´sniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), 647-657.
  13. S. Kanas, Coefficient estimate in subclasses of the Caratheodary class related to conic domains, Acta Math. Univ. Come- nianae LXXIV. 2 (2005), 149-161.
  14. F. R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8-12.
  15. A. K. Mishra and P. Gochhayat, A coefficient inequality for a sublclass of the Caratheodory functions defined using conical domains, Comput. Math. Appl. 61 (2011), 2816-2820.
  16. K. I. Noor and S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62 (2011), 2209-2217.
  17. K. I. Noor, On a generalization of uniformly convex and related functions, Comput. Math. Appl. 61 (2011), 117-125.
  18. K. I. Noor, M. Arif and M. W. Ul-Haq, On k-uniformly close-to-convex functions of complex order, Appl. Math. Comput. 215 (2009), 629-635.
  19. K. I. Noor, N. Khan and M. A. Noor, On generalized spiral-like analytic functions, Filomat, 28 (7) (2014), 1493-1503.
  20. K. I. Noor, On uniformly univalent functions with respect to symmetrical points, J. Math. Ineq. 2014 (2014), 1-14.
  21. K. I. Noor, Q. Z. Ahmad and M. A. Noor, On some subclasses of analytic functions defined by fractional derivative in the conic regions, Appl. Math. Inf., Sci. 9 (2) (2015), page 819.
  22. M. Obradovic and P. Ponnusanny, Radius of univalence of certain class of analytic functions, Filomat, 27 (2013), 1085-1090.
  23. K. Sakaguchi, On the theory of univalent mapping, J. Math. Soc. Japan, 11 (1959), 72-80.
  24. H. M. Srivastava, T. N. Shanmugam, C. Ramachandran and S. Sivassurbramanian, A new subclass of k-uniformly convex functions with negative coefficients, J. Inequal. Pure, Appl. Math. 8 (43) (2007), Art. ID 43.