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## Fixed point theory on spaces with vector-valued metrics and application

#### Bazine Safia [1] , Ellaggoune Fateh [2] , Aliouche Abdelkrim [3]

The purpose of this work is to prove some common fixed point theorems for two operators on a set endowed with one or two vector-valued metrics. The use of vector-valued metrics makes it possible for each equation of a system to have its own Lipschitz property, while the use of two such metrics makes it possible for the Lipschitz condition to be expressed with respect to an incomplete metric. An application is presented for a system of operatorial equations.
Fixed point, vector-valued metric, matrix convergent to zero
• G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16, 201-206, 1973.
• R. Kannan, Some remarks on fixed points, Bull. Calcutta Math. Soc. 60, 71-76, 1960.
• D. O'Regan, R. Precup, Continuation theory for contractions on spaces with two vector- valued metrics, Applicable Analysis. 82, 131-144, 2003.
• A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Dier. Uvavn. 2, 115-134, 1964.
• R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49, no. 3-4, 703-708, 2009.
• S. Reich, Some results concerning contraction mappings, Canad. Math. Bull. 14, 121-124, 1971.
• I. A. Rus, Principles and applications of the Fixed Point Theory, Dacia, Cluj-Napoca, Romania, 1979.
• M. Turinici, Finite-dimensional vector contractions and their fixed points, Studia Universitatis Babeş-Bolyai. Mathematica, 35, no. 1, 30-42, 1990.
• R. S. Varga, Matrix Iterative Analysis, vol. 27 of Springer Series in Computational Mathematics Springer, Berlin, Germany, 2000.
Birincil Dil en Matematik Matematik Yazar: Bazine Safia Yazar: Ellaggoune Fateh Yazar: Aliouche Abdelkrim Yayımlanma Tarihi : 1 Haziran 2017
 Bibtex @araştırma makalesi { hujms451009, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2017}, volume = {46}, pages = {419 - 426}, doi = {}, title = {Fixed point theory on spaces with vector-valued metrics and application}, key = {cite}, author = {Safia, Bazine and Fateh, Ellaggoune and Abdelkrim, Aliouche} } APA Safia, B , Fateh, E , Abdelkrim, A . (2017). Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics , 46 (3) , 419-426 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/38758/451009 MLA Safia, B , Fateh, E , Abdelkrim, A . "Fixed point theory on spaces with vector-valued metrics and application". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 419-426 Chicago Safia, B , Fateh, E , Abdelkrim, A . "Fixed point theory on spaces with vector-valued metrics and application". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 419-426 RIS TY - JOUR T1 - Fixed point theory on spaces with vector-valued metrics and application AU - Bazine Safia , Ellaggoune Fateh , Aliouche Abdelkrim Y1 - 2017 PY - 2017 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 419 EP - 426 VL - 46 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Fixed point theory on spaces with vector-valued metrics and application %A Bazine Safia , Ellaggoune Fateh , Aliouche Abdelkrim %T Fixed point theory on spaces with vector-valued metrics and application %D 2017 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 46 %N 3 %R %U ISNAD Safia, Bazine , Fateh, Ellaggoune , Abdelkrim, Aliouche . "Fixed point theory on spaces with vector-valued metrics and application". Hacettepe Journal of Mathematics and Statistics 46 / 3 (Haziran 2017): 419-426 . AMA Safia B , Fateh E , Abdelkrim A . Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 419-426. Vancouver Safia B , Fateh E , Abdelkrim A . Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 426-419.