A two-parameter control for contractive-like multivalued mappings (Q409705)
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scientific article; zbMATH DE number 6024171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A two-parameter control for contractive-like multivalued mappings |
scientific article; zbMATH DE number 6024171 |
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A two-parameter control for contractive-like multivalued mappings (English)
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13 April 2012
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fixed point
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multivalued contraction
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Picard iteration
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(\(\alpha\),\(\beta\))-contraction mapping
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complete metric space
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lower semicontinuous function
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closed-valued contraction
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Hausdorff distance
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In this very interesting paper, the author presents some fixed point theorems for a new class of contractive type multivalued mappings, namely, the so-called (\(\alpha\),\(\beta\))-contraction mappings (where \(\alpha\) and \(\beta\) are two functions on \([0,\infty)\)).NEWLINENEWLINEThe main purpose of this paper is to show that the Nadler contraction condition on a multivalued operator \(F\) is too restrictive for a successful construction of a Picard sequence of successive approximations which would converge to a fixed point of \(F\). Some nice examples are accompanying the theoretical result.
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