| Title:
|
Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets (English) |
| Author:
|
Banaś, Józef |
| Author:
|
Ben Amar, Afif |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
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54 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
21-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove a collection of new fixed point theorems for operators of the form $T+S$ on an unbounded closed convex subset of a Hausdorff topological vector space $(E,\Gamma)$. We also introduce the concept of demi-$\tau$-compact operator and $\tau$-semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel'skii type is proved for the sum $T+S$ of two operators, where $T$ is $\tau$-sequentially continuous and $\tau$-compact while $S$ is $\tau$-sequentially continuous (and $\Phi_{\tau}$-condensing, $\Phi_{\tau}$-nonexpansive or nonlinear contraction or nonexpansive). The main condition in our results is formulated in terms of axiomatic $\tau$-measures of noncompactness. Apart from that we show the applicability of some our results to the theory of integral equations in the Lebesgue space. (English) |
| Keyword:
|
$\tau$-measure of noncompactness |
| Keyword:
|
$\tau$-sequential continuity |
| Keyword:
|
$\Phi_{\tau}$-condensing operator |
| Keyword:
|
$\Phi_{\tau}$-nonexpansive operator |
| Keyword:
|
nonlinear contraction |
| Keyword:
|
fixed point theorem |
| Keyword:
|
demi-$\tau$-compactness |
| Keyword:
|
operator $\tau$-semi-closed at origin |
| Keyword:
|
Lebesgue space |
| Keyword:
|
integral equation |
| MSC:
|
47H10 |
| idMR:
|
MR3038069 |
| . |
| Date available:
|
2013-02-21T14:01:16Z |
| Last updated:
|
2015-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143150 |
| . |
| Reference:
|
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