Journal of Convex Analysis 32 (2025), No. 2, 605--630
Copyright Heldermann Verlag 2025
Near Convexity and Generalized Differentiation
Nguyen Mau Nam
Fariborz Maseeh Dept. of Mathematics & Statistics, Portland State University, Portland, U.S.A.
mnn3@pdx.edu
Nguyen Nang Thieu
(1) Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
(2) The State University of New York, Incheon, South Korea
nnthieu@math.ac.vn
Nguyen Dong Yen
Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
ndyen@math.ac.vn
We introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex set-valued mappings and nearly convex functions. Our contributions expand the current knowledge of nearly convex sets and functions, while providing several new results involving nearly convex set-valued mappings.
Keywords: Relative interior, nearly convex set, nearly convex function, nearly convex set-valued mapping, subdifferential, normal cone, coderivative.
MSC: 49J52, 49J53, 90C31.
[ Fulltext-pdf (176 KB)] for subscribers only.