Results 1 to 10 of about 10,275,715 (164)

Characterization of Radially Lower Semicontinuous Pseudoconvex Functions [PDF]

Journal of Optimization Theory and Applications, 2020
A differentiable function is pseudoconvex if and only if its restrictions over straight lines are pseudoconvex. A differentiable function depending on one variable, defined on some closed interval [a, b] is pseudoconvex if and only if there exist some ...
V. I. Ivanov
semanticscholar   +8 more sources

Pseudoconvex classes of functions. I. Pseudoconcave and pseudoconvex sets [PDF]

Pacific Journal of Mathematics, 1988
An axiomatic definition of a pseudoconvex class of functions is developed. The models include classes of subharmonic, plurisubhar- monic, g-plurisubharmonic, convex and ^-convex functions, and many others. Notions of dual class of functions and of pseudoconcave and pseudoconvex sets are introduced and studied. The results have appli- cations to complex
Zbigniew Słodkowski
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Comparison and localization of invariant functions on strongly pseudoconvex domains [PDF]

Bulletin of the London Mathematical Society, 2022
Comparison and localization results for the Lempert function, the Carathéodory distance, and their infinitesimal forms on strongly pseudoconvex domains are obtained. Related results for visible and strongly complete domains are proved.
N. Nikolov
semanticscholar   +3 more sources

Families of Strictly Pseudoconvex Domains and Peak Functions. [PDF]

J Geom Anal, 2018
We prove that given a family $(G_t)$ of strictly pseudoconvex domains varying in $\mathcal{C}^2$ topology on domains, there exists a continuously varying family of peak functions $h_{t, }$ for all $G_t$ at every $ \in\partial G_t.$
Lewandowski A.
europepmc   +7 more sources

On pseudoconvex functions and applications to global optimization [PDF]

ESAIM: Proceedings, 2007
In this paper, we characterize pseudoconvex functions using an abstract subdifierential. As applications, we also characterize maxima of pseudoconvex functions, and we study some fractional and quadratic optimization problems. Resume. Nous caracterisons des fonctions pseudoconvexes en utilisant un sous difierentiel abstrait.
A. Hassouni, A. Jaddar
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On the pseudoconvexity and pseudolinearity of some classes of fractional functions [PDF]

Optimization, 2007
The aim of the article is to study the pseudoconvexity (pseudoconcavity) of the ratio between a quadratic function and the square of an affine function. Applying the Charnes–Cooper transformation of variables the function is transformed in a quadratic one defined on a suitable halfspace.
Laura Carosi, Laura Martein
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The Zeros of Holomorphic Functions in Strictly Pseudoconvex Domains [PDF]

Transactions of the American Mathematical Society, 1975
We determine a sufficient condition on a positive divisor in certain strictly pseudoconvex domains in C n {{\mathbf {C}}^n} such that there exists a function in the Nevanlinna class which determines the divisor.
Lawrence Gruman
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Generalized Pseudoconvex Functions and Multiobjective Programming

Journal of Mathematical Analysis and Applications, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R.N. Mukherjee
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Pseudoconvex classes of functions. III. Characterization of dual pseudoconvex classes on complex homogeneous spaces [PDF]

Transactions of the American Mathematical Society, 1988
Invariant classes of functions on complex homogeneous spaces, with properties similar to those of the class of plurisubharmonic functions, are studied. The main tool is a regularization method for these classes, and the main theorem characterizes dual classes of functions (where duality is defined in terms of the local maximum property).
Zbigniew Słodkowski
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Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains. [PDF]

Proc Natl Acad Sci U S A, 1975
A strictly plurisubharmonic exhaustion function with negative values is constructed for arbitrary relatively compact pseudoconvex domains with smooth boundary in a Stein manifold. It is applied to verify the Serre conjecture in a special case. A sufficient condition is given that guarantees the existence of a neighborhood-basis of Stein domains for ...
Diederich K, Fornaess JE.
europepmc   +6 more sources