Vectorial variational principle with variable set-valued perturbation
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605461813 | ||
| 003 | CHVBK | ||
| 005 | 20210128100245.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150401xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-3587-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-3587-z | ||
| 245 | 0 | 0 | |a Vectorial variational principle with variable set-valued perturbation |h [Elektronische Daten] |c [Jian Zhang, Jing Qiu] |
| 520 | 3 | |a We give a general vectorial Ekeland's variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space. Being quite different from the previous versions of vectorial Ekeland's variational principle, the perturbation in our version is no longer only dependent on a fixed positive vector or a fixed family of positive vectors. It contains a family of set-valued functions taking values in the positive cone and a family of subadditive functions of topology generating quasi-metrics. Hence, the direction of the perturbation in the new version is a family of variable subsets which are dependent on the objective function values. The general version includes and improves a number of known versions of vectorial Ekeland's variational principle. From the general Ekeland's principle, we deduce the corresponding versions of Caristi-Kirk's fixed point theorem and Takahashi's nonconvex minimization theorem. Finally, we prove that all the three theorems are equivalent to each other. | |
| 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's variational principle |2 nationallicence | |
| 690 | 7 | |a F-type topological space |2 nationallicence | |
| 690 | 7 | |a locally convex space |2 nationallicence | |
| 690 | 7 | |a pre-ordered linear space |2 nationallicence | |
| 690 | 7 | |a direction of perturbation |2 nationallicence | |
| 700 | 1 | |a Zhang |D Jian |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, P. R. China |4 aut | |
| 700 | 1 | |a Qiu |D Jing |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, 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 31/4(2015-04-01), 595-614 |x 1439-8516 |q 31:4<595 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-3587-z |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/s10114-015-3587-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhang |D Jian |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Qiu |D Jing |u School of Mathematical Sciences, Soochow University, 215006, Suzhou, 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 31/4(2015-04-01), 595-614 |x 1439-8516 |q 31:4<595 |1 2015 |2 31 |o 10114 | ||