Convex extensions and envelopes of lower semi-continuous functions

2002 ◽  
Vol 93 (2) ◽  
pp. 247-263 ◽  
Author(s):  
Mohit Tawarmalani ◽  
Nikolaos V Sahinidis
Keyword(s):  
Continuous Functions ◽  
Lower Semi

The Multidirectional Mean Value Theorem in Banach Spaces

1997 ◽  
Vol 40 (1) ◽  
pp. 88-102 ◽  
Author(s):  
M. L. Radulescu ◽  
F. H. Clarke
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Continuous Functions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Locally Lipschitz Functions ◽  
Bump Function ◽  
Lipschitz Continuous ◽  
Lower Semi ◽  
Locally Lipschitz

AbstractRecently, F. H. Clarke and Y. Ledyaev established a multidirectional mean value theorem applicable to lower semi-continuous functions on Hilbert spaces, a result which turns out to be useful in many applications. We develop a variant of the result applicable to locally Lipschitz functions on certain Banach spaces, namely those that admit a C1-Lipschitz continuous bump function.

\(\mathcal{I}\)-Lower Semi Continuous Functions

2012 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
C. Ganesa Moorthy ◽  
P. Tamizharasi
Keyword(s):  
Continuous Functions ◽  
Lower Semi

scholarly journals Optimality Conditions for Lower Semi-continuous Functions

1996 ◽  
Vol 202 (2) ◽  
pp. 686-700 ◽  
Author(s):  
Chin Cheng Chou ◽  
Xinbao Li ◽  
Kung-Fu Ng ◽  
Shuzhong Shi
Keyword(s):  
Optimality Conditions ◽  
Continuous Functions ◽  
Lower Semi

SOME FIXED POINT RESULTS IN d-COMPLETE TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9837-9847
Author(s):  
S. Rathee ◽  
P. Gupta ◽  
V. Narayan Mishra
Keyword(s):  
Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Lower Semi

This paper aims to use T-orbitally lower semi-continuous and $w$-continuous functions in $d$-complete topological spaces to validate some fixed point theorems and extend various known results. The paper also seeks to establish, in the setting of $d$-complete topological spaces, Mizoguchi-Takahashi's type coincidence point theorem for single valued map. The results are supported by illustrative examples.

scholarly journals The subdifferential of the sum of two functions in Banach spaces II. Second order case

1995 ◽  
Vol 51 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Robert Deville ◽  
El Mahjoub El Haddad
Keyword(s):  
Hilbert Spaces ◽  
Type Theorem ◽  
Continuous Functions ◽  
Second Order ◽  
Infinite Dimensional ◽  
Jacobi Operators ◽  
Uniqueness Results ◽  
Lower Semi ◽  
Order Case ◽  
Jacobi Equations

We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.

scholarly journals Monotone insertion of semi-continuous functions on stratifiable spaces

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 575-584 ◽  
Author(s):  
Ying-Ying Jin ◽  
Li-Hong Xie ◽  
Hong-Wei Yue
Keyword(s):  
Continuous Function ◽  
Real Number ◽  
Continuous Functions ◽  
Lower Semi

In this paper, we consider the problem of inserting semi-continuous function above the (generalized) real-valued function in a monotone fashion. We provide some characterizations of stratifiable spaces, semi-stratifiable spaces, and k-monotonically countably metacompact spaces (k-MCM) and so on. It is established that: (1) A space X is k-MCM if and only if for each locally bounded real-valued function h : X ? R, there exists a lower semi-continuous and k-upper semi-continuous function h': X ? R such that (i) |h|? h', (ii) h'1 ? h'2 whenever |h1| ? |h2|. (2) A space X is stratifiable if and only if for each function h : X ? R* (R* is the generalized real number set), there is a lower semi-continuous function h' : X ? R

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