Error bounds of lower semi-continuous convex-along-rays functions

Document Type : Research Paper


1 Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran

2 Department of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Iran


In this paper, we study Lipschitz global error bounds for lower semi-continuous convex-along-rays (l.s.c. CAR) functions. We find a condition that ensures the existence of a global error bound for a CAR function. Moreover, we find a condition under which an l.s.c. CAR function does not have a Lipschitz global error bound. Finally, we survey Lipschitz's global error bounds of an l.s.c. (in particular, an l.s.c. CAR) function from the perspective of abstract convexity.


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Volume 14, Issue 10
October 2023
Pages 139-153
  • Receive Date: 04 June 2022
  • Revise Date: 12 January 2023
  • Accept Date: 05 February 2023