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Extensions of Minimization Theorems and Fixed Point Theorems on a Quasimetric Space

Abstract

We introduce the new concepts of -distance, -type mapping with respect to some -distance and -complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an -complete quasimetric space. We also give some examples of quasimetrics, -distances, and -type mapping with respect to some -distance. Our results extend, improve, and unify many known results due to Caristi, Ekeland, Ćirić, Kada-Suzuki-Takahashi, Ume, and others.

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Correspondence to Jeong Sheok Ume.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ume, J.S. Extensions of Minimization Theorems and Fixed Point Theorems on a Quasimetric Space. Fixed Point Theory Appl 2008, 230101 (2008). https://doi.org/10.1155/2008/230101

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  • DOI: https://doi.org/10.1155/2008/230101

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