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.


Articles in Press, Corrected Proof
Available Online from 24 February 2023
  • Receive Date: 04 June 2022
  • Revise Date: 12 January 2023
  • Accept Date: 05 February 2023
  • First Publish Date: 24 February 2023