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Multivalent Harmonic Uniformly Starlike Functions
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 3,  2009, pp.545-555
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.3.545
 Title & Authors
Multivalent Harmonic Uniformly Starlike Functions
Ahuja, Om; Joshi, Santosh; Sangle, Naveneet;
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In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.
harmonic functions;multivalent harmonic functions;convex combinations;distortion bounds;uniformly harmonic starlike;
 Cited by
O. P. Ahuja, R. Aghalary and S. B. Joshi, Harmonic univalent functions associated with k-uniformly starlike functions, Math. Sci. Res. J., 9(1)(2005), 9-17.

O. P. Ahuja and J. M. Jahangiri, Noshiro-type harmonic univalent functions, Scientiae Math. Japonicae, 56(2)(2002), 293-299.

O. P. Ahuja and J. M. Jahangiri, Multivalent harmonic starlike functions with missing coecients, Math. Sci. Res. J., 7(9)(2003), 347-352.

O. P. Ahuja and J. M. Jahangiri, On a linear combination of classes of multivalently harmonic functions, Kyungpook Math. J., 42(1)(2002), 61-70.

O. P. Ahuja and J. M. Jahangiri, Multivalent harmonic starlike functions, Ann. Univ. Mariae Curie-Sklodowska, Vol. LV, 1 Sectio A, 55(1)(2001), 1-13.

O. P. Ahuja and J. M. Jahangiri, Errata to "Multivalent harmonic starlike functions" [Univ. Mariae Curie-Sklodowska, Vol LV, sectio A, 55(1)(2001), 1-13]

O. P. Ahuja and J. M. Jahangiri, Errata to "Multivalent harmonic starlike functions" Univ. Mariae Curie-Sklodowska, Sectio. A, 56(1)(2002), 105.

M. K. Aouf, A generalization of multivalent functions with negative coefficient II, Bull Korean Math. Soc., 25(2)(1988), 221-232.

R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 25(1997), 17-32.

D. Bshouty, W. Hengartner and M. Naghibi-Beidokhti, p-valent harmonic mapping with finite Blaschke dilatations, Ann. Univ. Mariae Curie. Sklodowska Sectio. A, 53(2)(1999), 9-26.

J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acd. Aci. Fenn. Ser. A I Math., 9(1984), 3-25.

P. L. Duren, Harmonic mappings in the plane, Cambridge Tract in Mathematics (Cambridge: 156, Cambridge University Press), 2004, ISBN: 0-521-64121-73.

P. L. Duren, W. Hengartner and R. S. Laugesen, The argument principles harmonic functions, Amer. Math. Monthly, 103(5)(1996), 411-415. crossref(new window)

A. W. Goodman, On uniformly convex functions, Ann. Polon, Math., 56(1)(1991), 87-92.

A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl., 155(1991), 364-370. crossref(new window)

H. O. Guney and O. P. Ahuja, Inequalities involving multipliers for multivalent harmonic functions, J. Ineq. Pure Appl. Math., 7(5), Article 190, (2006), 1-9.

J. M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl., 235(1999), 470-477. crossref(new window)

J. M. Jahangiri, G. Murugusundaramoorthy and K. Vijaya, On starlikeness of certain multivalent Harmonic functions, Journal of Natural Geometry, 24(2003), 1-10.

S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform. Spect. Funct., 9(2)(2000), 121-132. crossref(new window)

W. Ma and D. Minda, Uniformly convex functions, Ann Polon Math., 57(1992), 165-175.

J. Patel, On a class of p-valent functions with negative and missing coefficients, Kyungpook Math. J., 36(1996), 29-40.

F. Ronning, On uniform starlikeness and related properties of univalent functions, Complex variables Theory Appl., 24(1994), 233-239. crossref(new window)

F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), 189-196. crossref(new window)

T. Rosy, B. A, Stephen, K. G. Subramanian and J. M. Jahangiri, Goodman-Ronning-Type harmonic univalent functions, Kyungpook Math. J., 41(2001), 45-54.

H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., 220(1998), 283-289. crossref(new window)

H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math., 28(1999), 275-284.