Existence and uniqueness of a solution for a minimization problem with a generic increasing function

A. M. Rubinov, A. J. Zaslavski
1999 Journal of the Australian Mathematical Society  
In this paper we study the existence and uniqueness of a solution for minimization problems with generic increasing functions in an ordered Banach space X. The standard approaches are not suitable in such a setting. We propose a new type of perturbation adjusted for the problem under consideration, prove the existence and point out sufficient conditions providing the uniqueness of a solution. These results are proved by assuming that the space X enjoys the following property: each decreasing
more » ... each decreasing norm-bounded sequence has a limit. We supply a counterexample, which shows that this property is essential and give a modification of obtained results for the space C(T), which does not possess this property. 1991 Mathematics subject classification (Amer. Math. Soc): primary 49J27, 90C30.
doi:10.1017/s1446788700000884 fatcat:yq2l3f5w7fbz3iety77oicu7ni