Surveys in Mathematics and its Applications
ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 4 (2009), 89 -- 97
MULTIVALUED PEROV-TYPE THEOREMS IN GENERALIZED METRIC SPACES
Abstract. In this paper we present some fixed point results for multivalued operators, which extend the ones given by A.I. Perov and A.V. Kribenko, as well as some recent contributions due to A. Bucur, L. Guran and A. Petruşel.2000 Mathematics Subject Classification: 47H10; 54H25.
Keywords: fixed point; multivalued operator; w-distance; Perov type generalized contraction.
A. Bucur, L. Guran and A. Petruşel, Fixed point theorems for multivalued operators on a set endowed with vector-valued metrics and applications, Fixed Point Theory, 10 (2009), No.1, 19-34.
O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica 44 (1996) 381-391. MR1416281(97j:49011). Zbl 0897.54029.
L. Guran, A multivalued Perov-type theorems in generalized metric spaces-accepted for publication in Creative Mathematics and Informatics, Baia-Mare, România.
A.I. Perov, On Cauchy problem for a system of ordinary differential equations, (in Russian), Priblizhen. Metody Reshen. Differ. Uravn., 2 (1964), 115-134. MR0216057(35#6892). Zbl 0196.34703.
A.I. Perov and A.V. Kibenko, On a certain general method for investigation of boundary value problems (Russian), Izv. Akad. Nauk SSSR Ser. Mat., 30 (1966), 249-264. MR0196534(33#4721). Zbl 0154.09201.
R. Precup, The role of the matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49 (2009), 703-708. MR2483647.
I.A. Rus, Principles and Applications of Fixed Point Theory, (in Romanian), Editura Dacia, Cluj-Napoca, 1979.
I.A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), 541-559. MR2464135. Zbl pre05505966.
I.A. Rus, A. Petruşel and G. Petruşel, Fixed Point Theory, Cluj University Press, 2008. MR2494238. Zbl pre05530321.
T. Suzuki and W. Takahashi, Fixed point theorems and characterizations of metric completeness, Topological Methods in Nonlinear Analysis, 8 (1996), 371-382. MR1483635(99c:54064). Zbl 0902.47050.
Department of Applied Mathematics,
Babeş-Bolyai University of Cluj-Napoca,
Kogălniceanu Street no. 1, 400084 Cluj-Napoca, Romania.
e-mail: firstname.lastname@example.org, email@example.com