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Open AccessArticle

New Generalized Mizoguchi-Takahashi’s Fixed Point Theorems for Essential Distances and e0-Metrics

1
School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
2
School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China
3
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1224; https://doi.org/10.3390/math7121224
Received: 9 November 2019 / Revised: 2 December 2019 / Accepted: 9 December 2019 / Published: 11 December 2019
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications)
In this paper, we present some new generalizations of Mizoguchi-Takahashi’s fixed point theorem which also improve and extend Du-Hung’s fixed point theorem. Some new examples illustrating our results are also given. By applying our new results, some new fixed point theorems for essential distances and e0-metrics were established. View Full-Text
Keywords: ℳ?-function; ℳ?(λ)-function; τ-function; essential distance (e-distance); e0-metric; Du-Hung’s fixed point theorem; Mizoguchi-Takahashi’s fixed point theorem; Nadler’s fixed point theorem; Banach contraction principle ℳ?-function; ℳ?(λ)-function; τ-function; essential distance (e-distance); e0-metric; Du-Hung’s fixed point theorem; Mizoguchi-Takahashi’s fixed point theorem; Nadler’s fixed point theorem; Banach contraction principle
MDPI and ACS Style

Jiang, B.; Huang, H.; Du, W.-S. New Generalized Mizoguchi-Takahashi’s Fixed Point Theorems for Essential Distances and e0-Metrics. Mathematics 2019, 7, 1224.

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