Document Details
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Document Type |
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Article In Journal |
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Document Title |
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On fixed points of quasi-contraction type multifunctions On fixed points of quasi-contraction type multifunctions |
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Subject |
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Mathematics |
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Document Language |
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English |
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Abstract |
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In 2009, Ilić and Rakoc ̌ević proved that quasi-contraction maps on normal cone metric spaces have a unique fixed point (Ilić and Rakoc ̌ević, 2009 ). Then, Kadelburg, Radenović and Rakoc ̌ević generalized their results by considering an additional assumption (Kadelburg et al., 2009 ). Also, they proved that quasi-contraction maps on cone metric spaces have the property (P) whenever λ ∈ (0, frac(1, 2)). Later, Haghi, Rezapour and Shahzad proved same results without the additional assumption and for λ ∈ (0, 1) by providing a new technical proof (Rezapour et al., 2010 ). In 2011, Wardowski published a paper (Wardowski, 2011 ) and tried to test fixed point results for multifunctions on normal cone metric spaces. Of course, he used a special view in his results. Recently, Amini-Harandi proved a result on the existence of fixed points of set-valued quasi-contraction maps in metric spaces by using the technique of Rezapour et al. (2010) . But, like Kadelburg et al. (2009), he could prove it only for λ ∈ (0, frac(1, 2)) (Amini-Harandi (2011) ). In this work, we prove again the main result of Amini-Harandi (2011) by using a simple method. Also, we introduce quasi-contraction type multifunctions and show that the main result of Amini-Harandi (2011) holds for quasi-contraction type multifunctions. |
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ISSN |
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0893-9659 |
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Journal Name |
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Applied Mathematics Letters |
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Volume |
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25 |
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Issue Number |
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5 |
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Publishing Year |
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1432 AH
2011 AD |
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Article Type |
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Article |
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Added Date |
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Sunday, February 19, 2012 |
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Researchers
| R Hamlbarani Haghi | Haghi, R Hamlbarani | Researcher | Doctorate | |
| Sh H Rezapour | Rezapour, Sh H | Researcher | Doctorate | |
| نصير شهزاد | Shahzad, Naseer | Researcher | Doctorate | naseer_shahzad@hotmail.com |
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