Fixed points for multivalued contractions with respect to a Pompeiu type metric
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Authors
Iulia Coroian
- Department of Land Measurements and Exact Sciences, University Of Agricultural Sciences and Veterinary Medicine, 3-5 Manastur St., 400372 Cluj-Napoca, Romania.
Abstract
The purpose of this paper is to present a fixed point theory for multivalued \(H^+\)-contractions from
the following perspectives: existence/uniqueness of the fixed and strict fixed points, data dependence of the fixed point set,
sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property for a multivalued operator, set-to-set operatorial equations and fractal operator theory.
Share and Cite
ISRP Style
Iulia Coroian, Fixed points for multivalued contractions with respect to a Pompeiu type metric, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 6084--6101
AMA Style
Coroian Iulia, Fixed points for multivalued contractions with respect to a Pompeiu type metric. J. Nonlinear Sci. Appl. (2017); 10(11):6084--6101
Chicago/Turabian Style
Coroian, Iulia. "Fixed points for multivalued contractions with respect to a Pompeiu type metric." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 6084--6101
Keywords
- \(H^{+}\)-type multivalued mapping
- Lipschitz equivalent metric
- multivalued operator
- contraction
MSC
References
-
[1]
J.-P. Aubin, H. Frankowska, Set-Valued Analysis , Birkhauser, Boston (1990)
-
[2]
C. Castaing, Sur les equations differentielles multivoques, C. R. Acad. Sci. Paris, 263 (1966), 63–66.
-
[3]
A. F. Filippov , Classical solutions of differential equations with multivalued right-hand side, SIAM J. Control, 5 (1967), 609–621.
-
[4]
M. Frigon, On continuation methods for contractive and nonexpansive mappings, Recent advances on metric fixed point theory, Univ. Sevilla, Seville (1996)
-
[5]
M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Frchet, Ann. Sci. Math. Qubec, 22 (1998), 161–168.
-
[6]
W. A. Kirk, N. Shahzad, Remarks on metrics transform and fixed point theorems, Fixed Point Theory Appl., 2013 (2013), 11 pages.
-
[7]
V. L. Lazăr, Fixed point theory for multivalued \(\phi\)-contractions, Fixed Point Theory Appl., 2011 (2011), 12 pages.
-
[8]
T. Lazăr, D. O’Regan, A. Petruşel, Fixed points and homotopy results for Ćirić-type multivalued operators on a set with two metrics, Bull. Korean Math. Soc., 45 (2008), 67–73.
-
[9]
T.-C. Lim , On fixed point stability for se-valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl., 110 (1985), 436–441.
-
[10]
J. T. Markin, Stability of solution sets for generalized differential equations, J. Math. Anal. Appl., 46 (1974), 289–291.
-
[11]
G. Moţ, A. Petruşel, G. Petruşel , Topics in Nonlinear Analysis and Applications to Mathematical Economics, Casa Cărţii de ştiinţa , Cluj-Napoca (2007)
-
[12]
H. K. Pathak, N. Shahzad , A new fixed point result and its application to existence theorem for nonconvex Hammerstein type integral inclusions, Electron. J. Qual. Theory Differ. Equ., 2012 (2012), 13 pages.
-
[13]
H. K. Pathak, N. Shahzad, A generalization of Nadler’s fixed point theorem and its application to nonconvex integral inclusions, Topol. Methods Nonlinear Anal., 41 (2013), 207–227.
-
[14]
A. Petruşel, Multivalued weakly Picard operators and applications, Sci. Math. Jpn., 59 (2004), 169–202.
-
[15]
A. Petruşel, I. A. Rus , The theory of a metric fixed point theorem for multivalued operators, Yokohama Publ., Yokohama (2010)
-
[16]
I. A. Rus, Generalized Contraction and Applications, Cluj Univ. Press, Cluj-Napoca (2001)
-
[17]
I. A. Rus, M.-A. Şerban, Some generalizations of a Cauchy lemma and applications, Presa Univ. Clujeană, Cluj-Napoca (2008)