On a general class of multi-valued weakly Picard mappings |
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| Authors: | M?d?lina Berinde Vasile Berinde |
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| Affiliation: | a Department of Statistics, Forecast and Mathematics, Faculty of Economics and Business Administration, “Babes-Bolyai” University of Cluj-Napoca, 58-60 T. Mihali St., 400591 Cluj-Napoca, Romania
b Department of Mathematics and Computer Science, North University of Baia Mare, Victoriei 76, 430122 Baia Mare, Romania |
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| Abstract: | The concept of weak contraction from the case of single-valued mappings is extended to multi-valued mappings and then corresponding convergence theorems for the Picard iteration associated to a multi-valued weak contraction are obtained. The main results in this paper extend, improve and unify a multitude of classical results in the fixed point theory of single and multi-valued contractive mappings and also improve recent results from the paper [P.Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192 (1995), 655-666]. |
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| Keywords: | Metric space Hausdorff distance Multi-valued mapping Fixed point Weak contraction Weakly Picard operator |
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