scholarly journals Upper and Lower Semicontinuity of Impulsive Cocycle Attractors for Impulsive Nonautonomous Systems

2019 ◽  
Author(s):  
E. M. Bonotto ◽  
M. C. Bortolan ◽  
T. Caraballo ◽  
R. Collegari
Keyword(s):  
Lower Semicontinuity ◽  
Nonautonomous Systems ◽  
Upper And Lower Semicontinuity

scholarly journals Semicontinuity of the Solution Mapping to a Parametric Generalized Weak Ky Fan Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Y. D. Xu
Keyword(s):  
Lower Semicontinuity ◽  
Solution Set ◽  
Ky Fan Inequality ◽  
Nonlinear Scalarization ◽  
Solution Mapping ◽  
Ky Fan ◽  
Upper And Lower Semicontinuity

Under new assumptions, which do not contain any information about the solution set, the upper and lower semicontinuity of the solution mapping to a class of parametric generalized weak Ky Fan inequality are established by using a nonlinear scalarization technique. These results extend and improve the recent ones in the literature. Some examples are given to illustrate our results.

scholarly journals Continuity of the Solution Maps for Generalized Parametric Set-Valued Ky Fan Inequality Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Z. Y. Peng ◽  
X. B. Li
Keyword(s):  
Metric Space ◽  
Lower Semicontinuity ◽  
Ky Fan Inequality ◽  
Solution Maps ◽  
Linear Metric Space ◽  
Ky Fan ◽  
Upper And Lower Semicontinuity

Under new assumptions, we provide suffcient conditions for the (upper and lower) semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature (e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010). Some examples are given to illustrate our results.

scholarly journals Semicontinuity of multifunctions connected with optimization with respect to cones

1986 ◽  
Vol 40 (2) ◽  
pp. 183-193 ◽  
Author(s):  
Alicja Sterna-Karwat
Keyword(s):  
Lower Semicontinuity ◽  
Optimization Problems ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Upper And Lower Semicontinuity

AbstractThis paper studies topological upper and lower semicontinuity of the minimal value multifunction and the solution multifunction for optimization problems, which are defined in terms of cones, subject to perturbations in constraints. It extends the results of Tanino and Sawaragi to finite dimensions and one of Berge to multiple objective optimization problems.

scholarly journals Chain recurrence and discretisation

1997 ◽  
Vol 55 (1) ◽  
pp. 63-71 ◽  
Author(s):  
Barnabas M. Garay ◽  
Josef Hofbauer
Keyword(s):  
Lower Semicontinuity ◽  
Variable Stepsize ◽  
Chain Recurrence ◽  
Limit Sets ◽  
Chain Recurrent Set ◽  
Numerical Dynamics ◽  
Upper And Lower Semicontinuity ◽  
Recurrent Set

Upper and lower semicontinuity results for the chain recurrent set are shown to remain valid in numerical dynamics with constant stepsizes. It is also pointed out that the chain recurrent set contains numerical ω–limit sets for discretisations with a variable stepsize sequence approaching zero.

scholarly journals Decomposition of Topologies Which Characterize the Upper and Lower Semicontinuous Limits of Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Agata Caserta
Keyword(s):  
Continuous Function ◽  
Lower Semicontinuity ◽  
Pointwise Convergence ◽  
Lower Semicontinuous ◽  
Continuous Functions ◽  
Point Of View ◽  
Limit Function ◽  
Statistical Point ◽  
Upper And Lower Semicontinuity

We present a decomposition of two topologies which characterize the upper and lower semicontinuity of the limit function to visualize their hidden and opposite roles with respect to the upper and lower semicontinuity and consequently the continuity of the limit. We show that (from the statistical point of view) there is an asymmetric role of the upper and lower decomposition of the pointwise convergence with respect to the upper and lower decomposition of the sticking convergence and the semicontinuity of the limit. This role is completely hidden if we use the whole pointwise convergence. Moreover, thanks to this mirror effect played by these decompositions, the statistical pointwise convergence of a sequence of continuous functions to a continuous function in one of the two symmetric topologies, which are the decomposition of the sticking topology, automatically ensures the convergence in the whole sticking topology.

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