Results 191 to 200 of about 2,333 (219)

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
openaire   +1 more source

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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Harmonic functions in non-locally convex spaces

Archiv der Mathematik, 1988
Let X be a topological vector space which is p normable for some ...
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General Harmonic Convex Functions and Integral Inequalities

2016
In this chapter, we introduce the notion of general harmonic convex functions using an arbitrary auxiliary function \(g: \mathbb{R} \rightarrow \mathbb{R}\). We obtain several new integral inequalities for general harmonic convex functions. Special cases which can be derived from our main results are also discussed.
Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan, Sabah Iftikhar   +3 more
openaire   +1 more source

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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Harmonic Convex function and Harmonic Variational Inequalities

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