Coincidence point and fixed point theorems for rational contractions
Keywords:
Fixed point, common fixed point, multivalued operator, coincidence point.Abstract
The purpose of this work is to present some coincidence point theorems for singlevalued and multivalued rational contractions. A comparative study of different rational contraction conditions is also presented. Our results extend some recent theorems in the literature.
Mathematics Subject Classification (2010): 47H10, 54H25.
References
Cabrera, I., Harjani, J., Sadarangani, K., A fixed point theorem for contractions of rational type in partially ordered metric spaces, Annali dell'Universita di Ferrara, Sez. VII Sci. Mat., 59(2013), no. 2, 251-258.
Frigon, M., Granas, A., Resultats du type de Leray-Schauder pour les contractions multivoques, Topol. Methods Nonlinear Anal., 4(1994), 197-208.
Harjani, J., Lopez, B., Sadarangani, K., Common fixed point theorems for monotone generalized contractions satisfying a contractive condition of rational type in ordered metric spaces, Journal of Convex Analysis, 20(2013), no. 4, 919-935.
Hu, S., Papageorgiou, N.S., Handbook of Multivalued Analysis, Vol. I and II, Kluwer Acad. Publ., Dordrecht, 1997 and 1999.
Jaggi, D.S., Some unique fixed point theorems, Indian J. Pure Appl. Math., 8(1977), 223-230.
Khan, M.S., Swalech, M., Sessa, S., Fixed point theorems by altering distances between the points, Bull. Austral Mah. Soc., 30(1984), 1-9.
Kumam, P., Rouzkard, F., Imdad, M., Gopal, D., Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction, Abstract and Applied Analysis, Art. 2013, ID 206515, 9 pp.
Lazar, T.A., Petrusel, A., Shahzad, N., Fixed points for non-self operators and domain invariance theorems, Nonlinear Analysis, 70(2009), 117-125.
Morales, J.R., Rojas, E.M., Altering distance functions and fixed point theorems through rational expression, 2012, no. 2, 110-116.
Oprea, A., Fixed point theorems for multivalued generalized contractions of rational type in complete metric spaces, Creative Mathematics and Informatics, to appear.
Petrusel, A., Rus, I.A., The theory of a metric fixed point theorem for multivalued operators, Yokohama Publ., Yokohama, 2010, 161-175.
Samet, B., Yazidi, H., An extension of Banach fixed point theorem for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal., 3(26)(2009), 1265-1271.
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