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Keywords = Kirk’s lemma

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11 pages, 287 KiB  
Article
On Suzuki Mappings in Modular Spaces
by Andreea Bejenaru and Mihai Postolache
Symmetry 2019, 11(3), 319; https://doi.org/10.3390/sym11030319 - 3 Mar 2019
Cited by 15 | Viewed by 3079
Abstract
Inspired by Suzuki’s generalization for nonexpansive mappings, we define the ( C ) -property on modular spaces, and provide conditions concerning the fixed points of newly introduced class of mappings in this new framework. In addition, Kirk’s Lemma is extended to modular spaces. [...] Read more.
Inspired by Suzuki’s generalization for nonexpansive mappings, we define the ( C ) -property on modular spaces, and provide conditions concerning the fixed points of newly introduced class of mappings in this new framework. In addition, Kirk’s Lemma is extended to modular spaces. The main outcomes extend the classical results on Banach spaces. The major contribution consists of providing inspired arguments to compensate the absence of subadditivity in the case of modulars. The results herein are supported by illustrative examples. Full article
(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)
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