Regularity properties for convex-like $C(T)$-valued functions on Hilbert spaces

نویسندگان
Moghimi, Gholamreza ID 1
Behroozizadeh, Elham ID 2
Izadi, Zeinab ID 3
Izadi, Javad ID 4

1 Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

2 Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

3 Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

4 Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

doi
10.22075/ijnaa.2024.33909.5061
چکیده

In this paper, we introduce several regularity properties for the non-differentiable convex-like $C(T)$-valued functions which are defined on a Hilbert space.  The relationships with various regularity properties are investigated. All results are given in terms of the convex subdifferential. Non-trivial numerical examples are incorporated to demonstrate the validity of the results established in this paper. To the best of our knowledge, this paper is the first to investigate the regularity properties for the $C(T)$-valued functions, even in the differentiable case of finite-dimensional spaces.

کلیدواژه‌ها
$C(T)$-valued function, Regularity property, Hilbert space, Convex subdifferential