In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].
Abstract:In this study, we establish that both the Mann and Ishikawa iteration processes are T-stable for the mappings T satisfying a more general contractive definition than that of Osilike [1] . The results obtained generalize some of the recent results of Osilike [1] which are themselves generalizations and extensions of some of the results of Harder and Hicks [2] and Rhoades [3,4] .
In this paper, we prove some fixed point theorems of Ćirić type for mappings having non-unique fixed points by employing rational-type contractive conditions and the notion of comparison functions. Our results are generalizations, extensions and improvements of some previous and corresponding results in the literature.
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