• Title/Summary/Keyword: Convex harmonic functions

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ON F-HARMONIC MAPS AND CONVEX FUNCTIONS

  • Kang, Tae-Ho
    • East Asian mathematical journal
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    • v.19 no.2
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    • pp.165-171
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    • 2003
  • We show that any F-harmonic map from a compact manifold M to N is necessarily constant if N possesses a strictly-convex function, and prove 'Liouville type theorems' for F-harmonic maps. Finally, when the target manifold is the real line, we get a result for F-subharmonic functions.

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LAZHAR TYPE INEQUALITIES FOR p-CONVEX FUNCTIONS

  • Toplu, Tekin;Iscan, Imdat;Maden, Selahattin
    • Honam Mathematical Journal
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    • v.44 no.3
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    • pp.360-369
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    • 2022
  • The aim of this study is to establish some new Jensen and Lazhar type inequalities for p-convex function that is a generalization of convex and harmonic convex functions. The results obtained here are reduced to the results obtained earlier in the literature for convex and harmonic convex functions in special cases.

CONSTRUCTION OF SUBCLASSES OF UNIVALENT HARMONIC MAPPINGS

  • Nagpal, Sumit;Ravichandran, V.
    • Journal of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.567-592
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    • 2014
  • Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.

SOME INCLUSION RELATIONS OF CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH GENERALIZED DISTRIBUTION SERIES

  • Magesh, Nanjundan;Porwal, Saurabh;Themangani, Rajavadivelu
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.843-854
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    • 2020
  • The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

HARMONIC MEROMORPHIC STARLIKE FUNCTIONS

  • Jahangiri, Jay, M.
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.291-301
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    • 2000
  • We give sufficient coefficient conditions for a class of meromorphic univalent harmonic functions that are starlike of some order. Furthermore, it is shown that these conditions are also necessary when the coefficients of the analytic part of the function are positive and the coefficients of the co-analytic part of the function are negative. Extreme points, convolution and convex combination conditions for these classes are also determined. Fianlly, comparable results are given for the convex analogue.

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Coefficient Bounds for a Subclass of Harmonic Mappings Convex in One Direction

  • Shabani, Mohammad Mehdi;Yazdi, Maryam;Sababe, Saeed Hashemi
    • Kyungpook Mathematical Journal
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    • v.61 no.2
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    • pp.269-278
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    • 2021
  • In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0, 𝜋). We find bounds for |fz(z)|, ${\mid}f_{\bar{z}}(z){\mid}$ and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction.

SHARP HEREDITARY CONVEX RADIUS OF CONVEX HARMONIC MAPPINGS UNDER AN INTEGRAL OPERATOR

  • Cheny, Xingdi;Mu, Jingjing
    • Korean Journal of Mathematics
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    • v.24 no.3
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    • pp.369-374
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    • 2016
  • In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+{\bar{f_x(z)}}$ under the integral operator $I_f(z)={\int_{o}^{z}}{\frac{f_1(u)}{u}}du+{\bar{{\int_{o}^{z}}{\frac{f_x(u)}{u}}}}$ and obtain the sharp constant ${\frac{{\sqrt[4]{6}}-{\sqrt[]{15}}}{9}}$, which generalized the result corresponding to the class of analytic functions given by Nash.

MEROMOR0PHIC UNIVALENT HARMONIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • Jahangiri, Jay M.;Silverman, Herb
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.763-770
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    • 1999
  • The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $$\mid$z$\mid$$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

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