Results 191 to 200 of about 2,343 (229)

On Harmonic Close-To-Convex Functions

Computational Methods and Function Theory, 2012
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Ponnusamy, Saminathan, Kaliraj, Anbareeswaran Sairam   +1 more
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p-Harmonic Maps and Convex Functions

Geometriae Dedicata, 1999
The following theorem is proved. Let \(M\) be a complete noncompact Riemannian manifold, \(N\) a simply connected Riemannian manifold of nonpositive curvature, and \(\varphi:M\to N\) a \(C^1\) \(p\)-harmonic map. Then \(\varphi\) is constant, provided that \(\int_M\|d\varphi \|^{p-1}< \infty\).
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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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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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Convex subclass of harmonic starlike functions

Applied Mathematics and Computation, 2004
A complex valued harmonic function \(f\) defined in a simply connected domain \(\Omega\) can be represented as \(f = h + \overline{g}\), where \(h\) and \(g\) are holomorphic in \(\Omega\). Such an \(f\) is locally univalent and sense preserving in \(\Omega \) if and only if \(|h'(z)| > |g'(z)|\) in \(\Omega\).
Yalcin, Sibel, Yamankaradeniz, M, Ozturk, M   +2 more
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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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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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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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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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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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