Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Relative interior
  • nearly convex set
  • nearly convex function
  • nearly convex set-valued mapping
  • subdifferential
  • normal cone
  • coderivative

Mathematics Subject Classification

49J52, 49J53, 90C31

Suggested citation

N. M. Nam, N. N. Thieu, N. D. Yen. “Near Convexity and Generalized Differentiation.” Journal of Convex Analysis 32 (2025), No. 2, 605–630.

Copyright Heldermann Verlag 2025