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Journal of Function Spaces
Volume 2016, Article ID 7123907, 6 pages
http://dx.doi.org/10.1155/2016/7123907
Research Article

A Subclass of Harmonic Functions Related to a Convolution Operator

1Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad Campus, Abbottabad, Pakistan
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 23 May 2016; Accepted 21 July 2016

Academic Editor: Wilfredo Urbina

Copyright © 2016 Saqib Hussain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Heinz, Über die Lösungen der Minimalflächengleichung, von Erhard Heinz, Vandenhoeck und Ruprecht, Göttingen, Germany, 1952.
  2. A. Weitsman, “On univalent harmonic mappings and minimal surfaces,” Pacific Journal of Mathematics, vol. 192, no. 1, pp. 191–200, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. J. Clunie and T. Sheil-Small, “Harmonic univalent functions,” Annales Academiae Scientiarum Fennicae A, vol. 9, pp. 3–25, 1984. View at Google Scholar
  4. J. M. Jahangiri, “Harmonic functions starlike in unit dics,” Journal of Mathematical Analysis and Applications, vol. 235, no. 2, pp. 470–477, 1999. View at Publisher · View at Google Scholar
  5. H. Silverman and E. M. Silvia, “Subclasses of harmonic univalent functions,” The New Zealand Journal of Mathematics, vol. 28, no. 2, pp. 275–284, 1999. View at Google Scholar · View at MathSciNet
  6. H. Silverman, “Harmonic univalent functions with negative coefficients,” Journal of Mathematical Analysis and Applications, vol. 220, no. 1, pp. 283–289, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. E. M. Wright, “The asymptotic expansion of the generalized hypergeometric function,” Proceedings of the London Mathematical Society, vol. 46, pp. 389–408, 1946. View at Google Scholar
  8. J. Dziok and H. M. Srivastava, “Certain subclasses of analytic functions associated with the generalized hypergeometric function,” Integral Transforms and Special Functions, vol. 14, no. 1, pp. 7–18, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Dzoik and H. M. Srivastava, “Class of analytic associated with generalized hypergeometric function,” Applied Mathematics and Computation, vol. 103, pp. 1–13, 1999. View at Google Scholar
  10. J. Dzoik and H. M. Srivastava, “Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function,” Advanced Studies in Contemporary Mathematics, vol. 5, no. 2, pp. 115–125, 2002. View at Google Scholar
  11. B. C. Carlson and D. B. Shaffer, “Starlike and prestarlike hypergeometric functions,” SIAM Journal on Mathematical Analysis, vol. 15, no. 4, pp. 737–745, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  12. S. D. Bernardi, “Convex and starlike univalent functions,” Transactions of the American Mathematical Society, vol. 135, pp. 429–446, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Dziok and R. K. Raina, “Families of analytic functions associated with the Wright generalized hypergeometric function,” Demonstratio Mathematica, vol. 37, no. 3, pp. 533–542, 2004. View at Google Scholar · View at MathSciNet
  14. O. P. Ahuja, S. Nagpal, and V. Ravichandran, “Radius constants for functions with the prescribed coefficient bounds,” Abstract and Applied Analysis, vol. 2014, Article ID 454152, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Y. Avci and E. Zlotkiewicz, “On harmonic univalent mappings,” Maria Curie-Skłodowska University, vol. 44, pp. 1–7, 1990. View at Google Scholar
  16. J. M. Jahangiri, “Coefficient bounds and univalance criteria for harmonic functions with negative coefficent,” Annales Academiae Scientiarum Fennicae A, pp. 57–66, 1998. View at Google Scholar
  17. J. M. Jahangiri, G. Murugusundaramoorthy, and K. Vijaya, “Starlikeness of Rucheweyh type harmonic univalent functions,” The Journal of the Indian Academy of Mathematics, vol. 26, no. 1, pp. 191–200, 2004. View at Google Scholar
  18. S. B. Joshi and M. Darus, “Uni.ed treatment for harmonic univalent functions,” Tamsui Oxford Journal of Information and Mathematical Sciences, vol. 24, no. 3, pp. 225–232, 2008. View at Google Scholar
  19. G. Murugusundaramoorthy, “A class of Ruscheweyh-type harmonic univalent functions with varying arguments,” Southwest Journal of Pure and Applied Mathematics, vol. 2, pp. 90–95, 2003. View at Google Scholar · View at MathSciNet
  20. T. Rosy, B. A. Stephen, K. G. Subramanian, and J. M. Jhangiri, “Goodman harmonic convex functions,” Journal of Natural Geometry, vol. 21, no. 1-2, pp. 39–50, 2001. View at Google Scholar
  21. J. Sokół, R. W. Ibrahim, M. Z. Ahmad, and H. F. Al-Janaby, “Inequalities of harmonic univalent functions with connections of hypergeometric functions,” Open Mathematics, vol. 13, no. 1, pp. 691–705, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. R. Chandrashekar, G. Murugusundaramoorthy, S. K. Lee, and K. G. Subramanian, “A class of complex valued harmonic functions de.ned by Dzoik Srivastava operator,” Chamchuri Journal of Mathematics, vol. 1, no. 2, pp. 31–42, 2009. View at Google Scholar