PEMETAAN KONTRAKSI CIRIC-MATKOWSKI PADA RUANG METRIK TERURUT

Mariatul Kiftiah

Abstract


In this paper, a new concept about Ciric-Matkowski contraction mapping in ordered metric space (related to ≤) is contructed. Different from the metric space, the Ciric-Matkowski contraction mapping in ordered metric space does not imply that the mapping to be continous. Next, some fixed point theorem of the Ciric-Matkowski contraction mapping in ordered metric space which is continous and not are proved. The result shows that the theorems do not guarantee the existence and uniqueness fixed point in ordered metric space. Adding comparable condition in it space then its mapping have a unique fixed point.

Keywords


fixed point,metric space,contraction mapping.

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References


Harjani, J., et al. 2011. Fixed Point Theorem for Meir-Keeler Contractions in ordered Metric spaces, Fixed Point Theory and Applications, 1 (83) 1-8.

J. Matkowski. 1980. Fixed point theorems for contractive mappings in metric spaces, Cas. Pest. Mat. (105)341–344.

Trotter, W.T. 1992. Combinatorics and Partially Ordered Sets: Dimension Theory. J. Hopkins University Press: U.S.

Royden, H.L. 1989. Real Analysis. 3rd ed. Macmillan Publishing Company: New York.

Ciric, L., 1981. A New Fixed-Point Theorem For Contractive Mappings. Publications De L’Institut Mathematique (N.S). 30 (44), 25–27

Meir, A, Keeler. E. 1969. A Theorem On Contraction Mappings. Journal of Mathematical Analysis and Applications. (28)326–329.14




DOI: https://doi.org/10.20527/epsilon.v8i2.107

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