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

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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. https://doi.org/10.68381/jca32030

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Published by Heldermann Verlag, 2025. Rights now held by Banach Press LLC.