On Caristi-Type Fixed Point Theorem in Cone Metric Space and Application
Samih Lazaiz *
Laboratory of Algebra Analysis and Applications, Department of Mathematics and Computer Science, Faculty of Sciences Ben MSik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco.
Mohamed Aamri
Laboratory of Algebra Analysis and Applications, Department of Mathematics and Computer Science, Faculty of Sciences Ben MSik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco.
Omar Zakary
Laboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben MSik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco.
*Author to whom correspondence should be addressed.
Abstract
The aim of this paper is to generalize Caristi's fixed point theorem. For that we extend the Száz maximum principle in normed space and, we introduce a new class of functions which generalize the notion of dominated function in Caristi's fixed point theorem. As a consequence, we obtain some common fixed point results.
Keywords: Cone metric space, Caristi's fixed point theorem, lower semi continuity, strongly minihedral cone, continuous cone