Ume, Jeong Sheok Extensions of minimization theorems and fixed point theorems on a quasimetric space. (English) Zbl 1157.49022 Fixed Point Theory Appl. 2008, Article ID 230101, 15 p. (2008). Summary: We introduce the new concepts of \(e\)-distance, \(e\)-type mapping with respect to some \(e\)-distance and \(S\)-complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an \(S\)-complete quasimetric space. We also give some examples of quasimetrics, \(e\)-distances, and \(e\)-type mapping with respect to some \(e\)-distance. Our results extend, improve, and unify many known results due to Caristi, Ekeland, Ćirić, Kada-Suzuki-Takahashi, Ume, and others. Cited in 2 Documents MSC: 49J52 Nonsmooth analysis 47H10 Fixed-point theorems 49J27 Existence theories for problems in abstract spaces Keywords:\(S\)-complete quasimetric space; minimization theorems; fixed point theorems; variational principles PDFBibTeX XMLCite \textit{J. S. Ume}, Fixed Point Theory Appl. 2008, Article ID 230101, 15 p. (2008; Zbl 1157.49022) Full Text: DOI EuDML References: [1] doi:10.2307/1999724 · Zbl 0305.47029 · doi:10.2307/1999724 [2] doi:10.1090/S0273-0979-1979-14595-6 · Zbl 0441.49011 · doi:10.1090/S0273-0979-1979-14595-6 [6] doi:10.2307/2040075 · Zbl 0291.54056 · doi:10.2307/2040075 [7] doi:10.1006/jmaa.1998.6030 · Zbl 0917.54047 · doi:10.1006/jmaa.1998.6030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.