Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2017 (2017), Article ID 4015268, 4 pages
https://doi.org/10.1155/2017/4015268
Research Article

Convolutions of Harmonic Functions with Certain Dilatations

Mathematical Sciences, Kent State University, Burton, OH 44021-9500, USA

Correspondence should be addressed to Jay M. Jahangiri; ude.tnek@ignahajj

Received 1 October 2017; Accepted 13 November 2017; Published 29 November 2017

Academic Editor: Teodor Bulboaca

Copyright © 2017 Om P. Ahuja and Jay M. Jahangiri. 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. J. Clunie and T. Sheil-Small, “Harmonic univalent functions,” Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica, vol. 9, pp. 3–25, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  2. H. Lewy, “On the non-vanishing of the Jacobian in certain one-to-one mappings,” Bulletin (New Series) of the American Mathematical Society, vol. 42, no. 10, pp. 689–692, 1936. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. D. Bshouty and A. Lyzzaik, “Close-to-convexity criteria for planar harmonic mappings,” Complex Analysis and Operator Theory, vol. 5, no. 3, pp. 767–774, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S. Ruscheweyh and T. Sheil-Small, “Hadamard products of SCHlicht functions and the Polya-SCHoenberg conjecture,” Commentarii Mathematici Helvetici, vol. 48, pp. 119–135, 1973. View at Publisher · View at Google Scholar · View at MathSciNet
  5. O. P. Ahuja, J. M. Jahangiri, and H. Silverman, “Convolutions for special classes of harmonic univalent functions,” Applied Mathematics Letters, vol. 16, no. 6, pp. 905–909, 2003. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Bshouty, S. S. Joshi, and S. B. Joshi, “On close-to-convex harmonic mappings,” Complex Variables and Elliptic Equations, vol. 58, no. 9, pp. 1195–1199, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. W. Kaplan, “Close-to-convex schlicht functions,” Michigan Mathematical Journal, vol. 1, pp. 169–185, 1952. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. S. Miller and P. T. Mocanu, “Univalent solutions of Briot-Bouquet differential equations,” Journal of Differential Equations, vol. 56, no. 3, pp. 297–309, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  9. S. S. Miller and P. T. Mocanu, Differential Subordination—Theory and Applications, vol. 225 of Monorgraphs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2000.