Coupled fixed point theorems for Zamfirescu type operators in ordered generalized Kasahara spaces
Dedicated to Professor Ioan A. Rus on the occasion of his 80th anniversary
Keywords:
Coupled fixed point, ordered generalized Kasahara space, Zamfirescu type operator, matrix convergent to zero, sequence of successive approximations, premetric.Abstract
In this paper we give some coupled fixed point theorems for Zamfirescu type operators in ordered generalized Kasahara spaces (X;!; d;_), where d : X_ X ! Rm+ is a premetric. An application concerning the existence and uniqueness of solutions for systems of functional-integral equations is also given.
Mathematics Subject Classification (2010): 47H10, 54H25.
References
Allaire, G., Numerical Linear Algebra, Springer, New York, 2008.
Bota, M.F., Petrusel, A., Petrusel, G., Samet, B., Coupled fixed point theorems for single-valued operators in b-metric spaces, Fixed Point Theory Appl., (2015), DOI 10.1186/s13663-015-0482-3.
Filip, A.-D., Fixed Point Theory in Kasahara Spaces, Casa Cartii de Stiinta, Cluj-Napoca, 2015.
Frechet, M., Les espaces abstraits, Gauthier-Villars, Paris, 1928.
Kasahara, S., On some generalizations of the Banach contraction theorem, Publ. RIMS, Kyoto Univ., 12(1976), 427-437.
Perov, A.I., On Cauchy problem for a system of ordinary differential equations, Pviblizhen, Met. Reshen. Di_er. Uvavn., 2(1964), 115-134.
Petrusel, A., Petrusel, G., Samet, B., Yao, J.-C., Coupled fixed point theorems for symmetric contractions in b-metric spaces with applications to operator equation systems, Fixed Point Theory, 17(2016), no. 2, 457-476.
Rus, I.A., Principles and Applications of the Fixed Point Theory, (Romanian), Ed. Dacia, 1979.
Rus, I.A., Kasahara spaces, Sci. Math. Jpn., 72(2010), no. 1, 101-110.
Rus, I.A., Petrusel, A., Petrusel, G., Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.
Precup, R., The role of the matrices that are convergent to zero in the study of semilinear operator systems, Math. Comput. Modelling, 49(2009), 703-708.
Turinici, M., Finite dimensional vector contractions and their fixed points, Studia Univ. Babes-Bolyai Math., 35(1990), no.1, 30-42.
Varga, R.S., Matrix Iterative Analysis, Springer, Berlin, 2000.
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