Extensions of Minimization Theorems and Fixed Point Theorems on a Quasimetric Space
© Jeong Sheok Ume. 2008
Received: 16 March 2008
Accepted: 9 June 2008
Published: 12 June 2008
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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