Results 81 to 90 of about 1,294 (187)
Approximations by differences of lower semicontinuous functions [PDF]
Tatra Mountains Mathematical Publications, 2015 Abstract A classical theorem of W. Sierpiński, S. Mazurkiewicz and S. Kempisty says that the class of all differences of lower semicontinuous functions is uniformly dense in the space of all Baire-one functions. We show a generalization of this result to more general situations and derive an abstract theorem in the case of a binormal ...
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Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth
Boundary Value Problems, 2007 We show that every weak supersolution of a variable exponent -Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Hölder continuous.
Kinnunen Juha +2 more
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Lower semicontinuity of the Willmore functional for currents
Journal of Differential Geometry, 2009 The weak mean curvature is lower semicontinuous under weak convergence of varifolds that is if μk → μ weakly as varifolds then ‖ ~ Hμ ‖Lp(μ)≤ lim infk→∞ ‖ ~ Hμk ‖Lp(μk) . In contrast, if Tk → T weakly as integral currents then μT may not have locally bounded first variation even if ‖ ~ HμTk ‖L∞(μk) is bounded. In 1999, Luigi Ambrosio asked the question
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Classification of Lipschitz Derivatives in Terms of Semicontinuity and the Baire Limit Functions
Annales Mathematicae SilesianaeWe introduce the generalized notion of semicontinuity of a function defined on a topological space and derive the useful classification of the so-called Lipschitz derivatives of functions defined on a metric space.
Maslyuchenko Oleksandr V. +1 more
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Abstract and Applied Analysis, 2016 Let X be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space X⁎. Let T:X⊇D(T)→2X⁎ and A:X⊇D(A)→2X⁎ be maximal monotone operators.
Teffera M. Asfaw
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On Fr\'{e}chet Subdifferential of Supremum for Arbitrary Family of Continuous Functions
Известия Иркутского государственного университета: Серия "Математика"The paper focuses on the Fr\'{e}chet subdifferential of the pointwise supremum of the family of functions taken over arbitrary index sets. The all functions in the corresponding family are defined on a Fr\'{e}chet smooth space; this class of Banach ...
D. V. Khlopin
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EURO Journal on Computational OptimizationModeling parts of an optimization problem as an optimal value function that depends on a top-level decision variable is a regular occurrence in optimization and an essential ingredient for methods such as Benders Decomposition.
Markus Gabl, Immanuel M. Bomze
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Common Fixed Point of Multivalued Generalized
Fixed Point Theory and Applications, 2010 Fixed point and coincidence results are presented for multivalued generalized -weak contractive mappings on complete metric spaces, where is a lower semicontinuous function with and for all . Our results extend previous results by Zhang and Song
Moradi Sirous, Djafari Rouhani Behzad
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Weak Convergence of Robust Functions on Topological Groups
MathematicsThis paper introduces weak variants of level convergence (L-convergence) and epigraph convergence (E-convergence) for nets of level functions on general topological spaces, extending the classical metric and real-valued frameworks to ordered codomains ...
Víctor Ayala +2 more
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Saddle point theorems on generalized convex spaces
Journal of Inequalities and Applications, 2000 A sharpened extension of Komiya's saddle point theorem is obtained for generalized convex spaces. Moreover, we show that convexity of the involved sets in his theorem can be replaced by acyclicity, and continuity of the involved functions by lower and ...
Park Sehie, Kim In-sook
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