Afrah A. N. Abdou - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Mohammed Aljohani - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. Mohamed A. Khamsi - Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, U.S.A.
The purpose of this note is to give a natural approach to the extensions of the Banach contraction principle in metric spaces endowed with a partial order, a directed graph or a binary relation in terms of extended quasi-metric. This novel approach is new and may open the door to other new fixed point theorems. The case of multivalued mappings is also discussed and an analogue result to Nadler's fixed point theorem in extended quasi-metric spaces is given.
Afrah A. N. Abdou, Mohammed Aljohani, Mohamed A. Khamsi, A novel approach to Banach contraction principle in extended quasi-metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 3858--3863
Abdou Afrah A. N., Aljohani Mohammed, Khamsi Mohamed A., A novel approach to Banach contraction principle in extended quasi-metric spaces. J. Nonlinear Sci. Appl. (2016); 9(6):3858--3863
Abdou, Afrah A. N., Aljohani, Mohammed, Khamsi, Mohamed A.. "A novel approach to Banach contraction principle in extended quasi-metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 3858--3863
