Sequentially lower complete spaces and Ekeland's variational principle
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| 024 | 7 | 0 | |a 10.1007/s10114-015-4541-9 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4541-9 | ||
| 245 | 0 | 0 | |a Sequentially lower complete spaces and Ekeland's variational principle |h [Elektronische Daten] |c [Fei He, Jing-Hui Qiu] |
| 520 | 3 | |a By using sequentially lower complete spaces (see [Zhu, J., Wei, L., Zhu, C. C.: Caristi type coincidence point theorem in topological spaces. J. Applied Math., 2013, ID 902692 (2013)]), we give a new version of vectorial Ekeland's variational principle. In the new version, the objective function is defined on a sequentially lower complete space and taking values in a quasi-ordered locally convex space, and the perturbation consists of a weakly countably compact set and a non-negative function p which only needs to satisfy p(x, y) = 0 iff x = y. Here, the function p need not satisfy the subadditivity. From the new Ekeland's principle, we deduce a vectorial Caristi's fixed point theorem and a vectorial Takahashi's non-convex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. By considering some particular cases, we obtain a number of corollaries, which include some interesting versions of fixed point theorem. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Vectorial Ekeland variational principle |2 nationallicence | |
| 690 | 7 | |a vectorial Caristi's fixed point theorem |2 nationallicence | |
| 690 | 7 | |a vectorial Takahashi's non-convex minimization theorem |2 nationallicence | |
| 690 | 7 | |a locally convex space |2 nationallicence | |
| 690 | 7 | |a sequentially lower complete space |2 nationallicence | |
| 700 | 1 | |a He |D Fei |u School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, P. R. China |4 aut | |
| 700 | 1 | |a Qiu |D Jing-Hui |u School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/8(2015-08-01), 1289-1302 |x 1439-8516 |q 31:8<1289 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4541-9 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4541-9 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a He |D Fei |u School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Qiu |D Jing-Hui |u School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/8(2015-08-01), 1289-1302 |x 1439-8516 |q 31:8<1289 |1 2015 |2 31 |o 10114 | ||