ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS

Volume: 4 Number: 1 June 1, 2014
  • T. Hayami
EN

ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS

Abstract

For normalized harmonic functions f z = h z + g z in the open unit disk, a criterion on the analytic part h z for f z to be p-valent and sense-preserving is discussed. Furthermore, several illustrative examples and images of f z satisfying the obtained condition are enumerated.

Keywords

References

  1. Bshouty, D. and Lyzzaik, A., (2011), Close-to-convexity criteria for planar harmonic mappings, Com- plex Anal. Oper. Theory, 5, 767-774.
  2. Clunie, J. and Sheil-Small, T., (1984), Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9, 3-25.
  3. Duren, P. L., (2004), Harmonic Mappings in the Plane, Cambridge University Press, Cambridge.
  4. Goodman, A. W., (1983), Univalent Functions, Vol. I and Vol. II, Mariner Publishing Company, Tampa, Florida.
  5. Hayami, T. and Owa, S., (2011), Hypocycloid of n + 1 cusps harmonic function, Bull. Math. Anal. Appl., 3, 239-246.
  6. Hayami, T., (2012), Coefficient conditions for harmonic close-to-convex functions, Abstr. Appl. Anal., , Article ID 413965, 12 pp.
  7. Hayami, T., (2013), A sufficient condition for p-valently harmonic functions, Complex Var. Elliptic
  8. Equ., Published online. DOI : 10.1080/17476933.2013.826656.

Details

Primary Language

English

Subjects

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Journal Section

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Authors

T. Hayami This is me

Publication Date

June 1, 2014

Submission Date

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Acceptance Date

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Published in Issue

Year 2014 Volume: 4 Number: 1

APA
Hayami, T. (2014). ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS. TWMS Journal of Applied and Engineering Mathematics, 4(1), 50-55. https://izlik.org/JA24XT89DT
AMA
1.Hayami T. ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS. JAEM. 2014;4(1):50-55. https://izlik.org/JA24XT89DT
Chicago
Hayami, T. 2014. “ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS”. TWMS Journal of Applied and Engineering Mathematics 4 (1): 50-55. https://izlik.org/JA24XT89DT.
EndNote
Hayami T (June 1, 2014) ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS. TWMS Journal of Applied and Engineering Mathematics 4 1 50–55.
IEEE
[1]T. Hayami, “ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS”, JAEM, vol. 4, no. 1, pp. 50–55, June 2014, [Online]. Available: https://izlik.org/JA24XT89DT
ISNAD
Hayami, T. “ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS”. TWMS Journal of Applied and Engineering Mathematics 4/1 (June 1, 2014): 50-55. https://izlik.org/JA24XT89DT.
JAMA
1.Hayami T. ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS. JAEM. 2014;4:50–55.
MLA
Hayami, T. “ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS”. TWMS Journal of Applied and Engineering Mathematics, vol. 4, no. 1, June 2014, pp. 50-55, https://izlik.org/JA24XT89DT.
Vancouver
1.T. Hayami. ON A CRITERION FOR MULTIVALENT HARMONIC FUNCTIONS. JAEM [Internet]. 2014 Jun. 1;4(1):50-5. Available from: https://izlik.org/JA24XT89DT