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Original Articles

Subordination and superordination results for analytic functions with respect to symmetrical points

, &
Pages 65-79 | Received 16 Oct 2016, Published online: 15 Sep 2017

References

  • F.S. Alsarari and S. Latha, On certain subclasses with respect to (2j; k)-symmetric conjugate points, J. Rajasthan Acad. Phys. Sci. 13 (2014), 17–30.
  • H.S. Al-Amiri, D. Coman and P.T. Mocanu, Some properties of starlike functions with respect to symmetric conjugate points, Int. J. Math. Math. Sci. 18 (1995), 467–474.
  • M.K. Aouf, F.M. Al-Oboudi and M.M. Haidan, On some results of for λ-spirallike and λ-Robertson functions of complex order, Publ. Inst. Math. (Beograd) (N.S.) 77(91) (2005), 93–98.
  • M.K. Aouf and T. Bulboacă, Subordination and superordination properties of multivalent functions defined by certain integral operator, J. Franklin Inst. 347(3) (2010), 641–653.
  • S.Z.H. Bukhari, M. Nazir and M. Raza, Some generalisations of analytic functions with respect to 2k-symmetric conjugate points, Maejo Int. J. Sci. Technol. 10 (2016), 1–12.
  • S.Z.H. Bukhari, M. Raza and M. Nazir, Some generalizations of the class of analytic functions with respect to k-symmetric points, Hacet. J. Math. Stat. 45 (2016), 1–14.
  • T. Bulboacă, A class of subordination-preserving integral operators, Indag. Math. (N.S.) 13(3) (2002), 301–311.
  • T. Bulboacă, Classes of first-order differential subordinations, Demonstr. Math. 35(2) (2002), 287–292.
  • T. Bulboacă, Differential subordination and superordinations. Recent Results, House Sci. Book Publ., Cluj-Napoca, 2005.
  • A.W. Goodman, Univalent functions, Vol. I, Mariner Publishing House, Tampa, Florida, 1983.
  • W. Janowski, Some extremal problems for certain families of analytic functions, I, Ann. Polon. Math. 28 (1973), 297–326.
  • K.R. Karthikeyan, Some classes of analytic functions with respect to symmetric conjugate points, European J. Math. Sci. 2(2) (2013), 168–177.
  • S.S. Miller and P.T. Mocanu, Differential Subordination. Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York and Basel, 2000.
  • S.S. Miller and P.T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl. 48(10) (2003), 815–826.
  • A. Muhammad, Some differential subordination and superordination problems of symmetric functions, Rend. Sem. Mat. Univ. Politec. Torino. 69(3) (2011), 247–259.
  • A. Muhammad and A. Khattak, Some differential subordination and superodination properties of symmetric analytic functions involving Noor integral operator, Le Mathematiche 67 (2012), 77–92.
  • A. Muhammad and M. Saeed, On a differential subordination and superordination of new class of meromorphic functions, Le Mathematiche 69 (2014), 259–274.
  • M. Obradović, M.K. Aouf and S. Owa, On some results for starlike functions of complex order, Publ. Inst. Math. (Beograd) (N.S.) 46(60) (1989), 79–85.
  • M. Obradović and S. Owa, On certain properties for some classes of starlike functions, J. Math. Anal. Appl. 145(2) (1990), 357–364.
  • V. Ravichandran, Starlike and convex functions with respect to conjugate points, Acta Math. Acad. Paedagog. Nyházi (New Ser.) 20 (2004), 31–37
  • W.C. Royster, On the univalence of a certain integral, Michigan Math. J. 12(4) (1965), 385–387.
  • K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11(1) (1959), 72–75.
  • S. Shams, S.R. Kulkarni and J.M. Jahangiri, Subordination properties of p-valent functions defined by integral operators, Int. J. Math. Math. Sci. (2006), Art. ID 94572, 3 pp.
  • T.N. Shanmugam, C. Ramachandran, M. Darus and S. Sivasubramanian, Differential sandwich theorems for some sub classes of analytic functions involving a linear operator, Acta Math. Univ. Comenian. (N.S.) 74(2) (2007), 287–294.
  • T.N. Shanmugam, S. Sivasubramanian and H. Silverman, On sandwich theorems for some classes of analytic functions, Int. J. Math. Math. Sci. (2006), Art. ID 29684, 13 pp.
  • H. Shiraishi, S. Owa and H.M. Srivastava, Sufficient conditions for strongly Carathéodory functions, Comput. Math. Appl. 62 (2011), 2978–2987.
  • Y.J. Sim, O.S. Kwon, N.E. Cho and H.M. Srivastava, Some sets of sufficient conditions for Carathéodory functions, J. Comput. Anal. Appl. 21 (2016), 1243–1254.
  • H.M. Srivastava, M.R. Khan and M. Arif, Some subclasses of close-to-convex mappings associated with conic regions, Appl. Math. Comput. 285 (2016), 94–102.
  • J. Stankiewicz, Some remarks on functions starlike with respect to symmetric points, Ann. Univ. Mariae Curie-Sk-lodowska Sect. A 19 (1970), 53–59.
  • T.V. Sudharsan, P. Balasubrahmanyam and K.G. Subramanian, On functions starlike with respect to symmetric and conjugate points, Taiwanese J. Math. 2 (1998), 57–68.
  • Z.-G. Wang, A new subclass of quasi-convex functions with respect to k-symmetric points, Lobachevskii J. Math. 19 (2005), 41–50.
  • Z.-G. Wang and C.Y. Gao, On starlike and convex functions with respect to 2k-symmetric conjugate points, Tamsui Oxf. J. Math. Sci. 24 (2008), 277–287.
  • Z.-G. Wang and Y.P. Jiang, Some properties of certain subclasses of colse-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points, Bull. Iran. Math. Soc. 36(2) (2010), 217–238.

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