On [sigma]-porous and [Phi]-angle-small sets in metric spaces

• Autorzy: Rolewicz S.
• Języki publikacji: EN

Abstrakty

EN

It is shown that in metric spaces each [alpha, phi)-meagre set A is uniformly very porous and its index of uniform v-porosity is not smaller than [k-alpha/3k+alpha] provided that [phi] is a strictly k-monotone family of Lipschitz functions and [alpha] < k. The paper contains also conditions implying that a k-monotone family of Lipschitz functions is strictly k-monotone.

Słowa kluczowe

EN

porous set; k-monotone family of Lipschitz functions

PL

zbiór porowaty

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no. 3
• Strony: 671--681
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Rolewicz S.

• Mathematical Institute, Polish Academy of Sciences, Warsaw, Poland

Bibliografia

• Argonsky, S., and Bruckner, A. (1985/6) Local compactness and porosity in metric spaces. Real Exchange Analysis 11, 365 - 379.
• Pallaschke, D., and Rolewicz, S. (1997) Foundation of Mathematical Optimization. Mathematics and its Applications 388. Kluwer Academic Publishers, Dordrecht/Boston/London.
• Penot, J-P. (2003) Rotundity, smoothness and duality. Control and Cybernetics, 32, 4.
• Preiss, D., and Zajıcek, L. (1984a) Stronger estimates of smallness of sets of Frechet nondifferentiability of convex functions. Proc. 11-th Winter School, Suppl. Rend. Circ. Mat di Palermo. ser II, 3, 219 - 223.
• Preiss, D., and Zajıcek, L. (1984b) Frechet differentiation of convex functions in a Banach space with a separable dual. Proc. Amer. Math. Soc. 91, 202 - 204.
• Rolewicz, S. (1994) On Mazur Theorem for Lipschitz functions. Arch. der Math., 63, 535 - 540.
• Rolewicz, S. (1995) On Φ-differentiability of functions over metric spaces. Topological Methods of Non-linear Analysis 5, 229 - 236.
• Rolewicz, S. (1999) On α(·)-monotone multifunction and differentiability of γ-paraconvex functions. Stud. Math. 133, 29 - 37.
• Rolewicz, S. (2002) On α(·)-monotone multifunctions and differentiability of strongly α(·)-paraconvex functions. Control and Cybernetics 31, 3, 1-19.
• Rolewicz, S. (2003) On uniform Φ-subdifferentials (in preparation).
• Zajıcek, L. (1976) Sets of σ-porosity and sets of σ-porosity (q). Casopis Pest Mat. 101, 350 – 359
• Zajıcek, L. (1983) Differentiability of distance functions and points of multivaluedness of the metric projection in Banach spaces. Cechoslovak Math. ˇ Jour. 33(108), 292 - 308.
• Zajıcek, L. (1984) A generalization of an Ekeland-Lebourg theorem and differentiability of distance functions. Proc. 11-th Winter School, Suppl. Rend. Circ. Mat di Palermo ser II, 3, 403 - 410.
• Zajicek, L. (1987/8) Porosity and σ-porosity. Real Exchange Analysis 13, 314 – 350