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Weak condition for generalized multi-valued (f,α,β)-weak contraction mappings

By Wutiphol Sintunavarat and Poom Kumam

Abstract

AbstractIn 2007, Kamran [T. Kamran, Multivalued f-weakly Picard mappings, Nonlinear Anal. 67 (2007) 2289–2296] extended the notion of multi-valued mapping from weak contraction and generalized (α,L)-weak contraction to f-weak contraction and generalized multi-valued f-weak contraction. He also obtained some common fixed point theorems with the notion of T-weakly commuting at a coincidence point of a hybrid pair. In this paper, we can drop the condition of T-weakly commuting in Theorems 2.9 and 3.5 in [5]. We further extend the notion of generalized multi-valued f-weak contraction and introduce the notion of generalized multi-valued (f,α,β)-weak contraction. We also establish some coincidence and common fixed point theorems with generalized multi-valued (f,α,β)-weak contraction mappings. Our results extend and generalize several common fixed point theorems of many authors

Publisher: Elsevier Ltd.
Year: 2011
DOI identifier: 10.1016/j.aml.2010.10.042
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