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Maximal Classes For Lower And Upper Semicontinuous Strong Świątkowski Functions
Demonstratio Mathematica, 2014 In this paper, we characterize the maximal additive and multiplicative classes for lower and upper semicontinuous strong Świątkowsk functions and lower and upper semicontinuous extra strong Świątkowski functions.
Szczuka Paulina
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Some characterizations of error bound for non-lower semicontinuous functions
Journal of Inequalities and Applications, 2019 In this paper, we study the error bound of non-lower semicontinuous functions. First, we extend the concepts of strong slope and global slope to the non-lower semicontinuous functions.
Miantao Chao +2 more
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Some fixed-point theorems for a general class of mappings in modular G-metric spaces [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et ...
Godwin Amechi Okeke, Daniel Francis
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On the Lower Semicontinuity of Supremal Functionals [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2003 Summary: In this paper we study the lower semicontinuity problem for a supremal functional of the form \[ F(u,\Omega )= \underset {x\in \Omega } {\text{ess\,sup}} f(x,u(x),Du(x)) \] with respect to the strong convergence in \(L^\infty (\Omega )\), furnishing a comparison with the analogous theory developed by Serrin for integrals.
GORI, MICHELE, MAGGI, FRANCESCO
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Characterization of lower semicontinuous convex functions [PDF]
Proceedings of the American Mathematical Society, 1992 We prove that a lower semicontinuous function defined on a reflexive Banach space is convex if and only if its Clarke subdifferential is monotone.
Correa, R., Jofré, A., Thibault, L.
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Proximal gradient methods beyond monotony [PDF]
Journal of Nonsmooth Analysis and Optimization, 2023 We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal gradient methods,
Alberto De Marchi
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Weak Lower Semicontinuity of Integral Functionals and Applications [PDF]
SIAM Review, 2017 Minimization is a reoccurring theme in many mathematical disciplines ranging from pure to applied ones. Of particular importance is the minimization of integral functionals that is studied within the calculus of variations. Proofs of the existence of minimizers usually rely on a fine property of the involved functional called weak lower semicontinuity.
Barbora Benesová, Martin Kruzík
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On the ARG MIN multifunction for lower semicontinuous functions [PDF]
Proceedings of the American Mathematical Society, 1988 The epi-topology on the lower semicontinuous functions L ( X )
Beer, Gerald, Kenderov, Petar
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Axioms, 2022 The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in the various settings of spaces. In this paper, we consider the asymptotic behavior of the resolvents of a sequence of functions defined in a complete ...
Yasunori Kimura, Keisuke Shindo
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Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD [PDF]
Journal of Functional Analysis, 2021 In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is a skew symmetric matrix.
Friedrich M., Perugini M., Solombrino F.
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