Results 141 to 150 of about 196 (170)

Logarithmic Convexity for Supremum Norms of Harmonic Functions

Bulletin of the London Mathematical Society, 1994
The authors prove the following convexity property for supremum norms of harmonic functions. Let \(\Omega\) be a (connected) domain in \(\mathbb{R}^ n\) \((n\geq 2)\), \(\Omega_ 0 \subset \Omega\) a nonempty open subset and \(E\subset \Omega\) a compact subset (which may be just one point).
Korevaar, J., Meyers, J.L.H.
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Directional Convexity of Convolutions of Harmonic Functions with Certain Dilatations

Computational Methods and Function Theory, 2021
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Garg, Raj K., Dorff, Michael, Jahangiri, Jay M.   +2 more
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Completely Convex and Positive Harmonic Functions

SIAM Journal on Mathematical Analysis, 1975
A completely convex function is a positive real-valued function on a real interval whose even derivatives alternate in sign. The author shows that every completely convex function is the restriction to the real line of a positive harmonic function in a vertical strip which is completely convex in x for each y.
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A remark on convex functions andp-harmonic maps

Geometriae Dedicata, 1995
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Cheung, L.-F., Leung, P.-F.
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Convolution Properties of Convex Harmonic Functions

International Journal of Open Problems in Complex Analysis, 2012
In this paper, we examine the convolutions of convex harmonic functions with some other classes of univalent harmonic functions dened by certain coecient conditions and prove that such convolutions belong to some well known classes of univalent harmonic functions.
Raj Kumar, Sushma Gupta, Sukhjit Singh
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Estimates for Convex Integral Means of Harmonic Functions

Proceedings of the Edinburgh Mathematical Society, 2013
AbstractWe prove that if f is an integrable function on the unit sphere S in ℝn, g is its symmetric decreasing rearrangement and u, v are the harmonic extensions of f, g in the unit ball , then v has larger convex integral means over each sphere rS, 0 < r < 1, than u has.
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Sections of stable harmonic convex functions

Nonlinear Analysis: Theory, Methods & Applications, 2015
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Li, Liulan, Ponnusamy, Saminathan
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Harmonic Exponential Convex Functions and Inequalities

2019
In this chapter, we intend to introduce and study a new class of harmonic exponential h-convex functions. We show that this class includes several new and previously known classes of harmonic convex functions. We derive several Hermite–Hadamard type integral inequalities. Numerous special cases are also discussed.
Muhammad Uzair Awan, Muhammad Aslam Noor, Khalida Inayat Noor   +2 more
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On a Conjecture Relative to the Maxima of Harmonic Functions on Convex Domains

SIAM Journal on Mathematical Analysis, 1999
Let \(u\) be a harmonic function defined on a bounded Jordan domain \(\Omega \) and satisfying the mixed boundary conditions \(u=0\) on \(\Gamma_0\), \((\partial u/\partial n)=1\) on \(\Gamma_1\), where \(\Gamma_1 \) is composed by a finite mumber of arcs of \(\partial \Omega \) and \(\Gamma_0 =\partial \Omega \setminus \Gamma_1 \), the length of ...
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Some properties of harmonic convex and harmonic quasi-convex functions

International Journal of Mathematics Trends and Technology, 2018
Masood Ahmed Choudhary, ToseefAhmed Malik   +1 more
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