A generalization of some results on multi-valued weakly Picard mappings in b-metric space
2008
scientific article
english
- multi-valued weak contraction
- single-valued contractive mappings
EN In this paper, we establish some convergence results in a complete b-metric space for the Picard iteration associated to two multi-valued weak contractions by employing the concepts of monotone and comparison functions. Our results generalize and extend those of Berinde and Berinde [8], Daffer and Kaneko [15] and Nadler [27]. Theorem 2.1 in our paper generalizes Theorem 5 of Nadler [27] and a recent result of Berinde and Berinde [8], it also extends, improves and unifies several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Also, Theorem 2.3 is a generalization and extension of Theorem 5 of Nadler [27] as well as Theorem 4 of Berinde and Berinde [8].
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