Correspondence: zuozhanfei@139. com Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China Abstract We determine and estimate the Ptolemy constant of absolute normalized norms on R by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject C...

This paper is concerned with the sensitivities of function space oriented interior point approximations in parameter dependent optimization problems. For an abstract setting that covers control constrained optimal control problems, the convergence of interior point sensitivities to the sensitivities of the optimal solution is shown. Error bounds for Lq norms are derived and illustrated with num...

Correspondence: zuozhanfei@139. com Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China Abstract We determine and estimate the Ptolemy constant of absolute normalized norms on R by means of their corresponding continuous convex functions on [0, 1]. Moreover, the exact values were calculated in some concrete Banach spaces. 2000 Mathematics Subject C...

If our mutlidimensional vectors "live" in some appropriate multidimensional space (See Greenberg) we need some properties vector norms A natural question about a vector is, how "long" is it? We might want to know this for a physical reason, say mean velocity, or for an abstract comparision.