A local fixed point theorem for set-valued mappings on partial metric spaces


  • Abdessalem Benterki University of Blida ; University of Medea




Partial metric space, fixed point, set-valued mapping


The purpose of this paper is to study the existence and location of fixed points for pseudo-contractive-type set-valued mappings in the setting of partial metric spaces by using Bianchini-Grundolfi gauge functions.


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Author Biography

Abdessalem Benterki, University of Blida ; University of Medea

LAMDA-RO Laboratory, Department of Mathematics

LMP2M Laboratory


M. Abbas, B. Ali, and C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology Appl. 160 (2013), 553-563. https://doi.org/10.1016/j.topol.2013.01.006

T. Abdeljawad, E. Karapinar and K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett, 24 (2011), 1900-1904. https://doi.org/10.1016/j.aml.2011.05.014

R. P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge: Cambridge University Press, 2001. https://doi.org/10.1017/CBO9780511543005

I. Altun, F. Sola, and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), 2778-2785. https://doi.org/10.1016/j.topol.2010.08.017

H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl. 159 (2012), 3234-3242. https://doi.org/10.1016/j.topol.2012.06.012

V. Berinde, Iterative approximation of fixed points, Berlin: Springer, 2nd revised and enlarged ed., 2007. https://doi.org/10.1109/SYNASC.2007.49

A. L. Dontchev, Local convergence of the Newton method for generalized equations, C. R. Acad. Sci., Paris, Sér. I, 322 (1996), 327-331.

A. L. Dontchev and W. W. Hager, An inverse mapping theorem for set-valued maps, Proc. Am. Math. Soc. 121 (1994), 481-489. https://doi.org/10.1090/S0002-9939-1994-1215027-7

W.-S. Du, E. Karapinar and N. Shahzad, The study of fixed point theory for various multivalued non-self-maps, Abstr. Appl. Anal. 2013 (2013), Article ID 938724, 9 pages. https://doi.org/10.1155/2013/938724

P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities, Ann. Oper. Res. 44 (1993), 7-42. https://doi.org/10.1007/BF02073589

M. C. Ferris and J. S. Pang, Engineering and economic applications of complementarity problems, Siam Rev. 39 (1997), 669-713. https://doi.org/10.1137/S0036144595285963

M. H. Geoffroy, S. Hilout, and A. Pietrus, Acceleration of convergence in Donchev's iterative method for solving variational inclusions, Serdica Math. J. 29 (2003), 45-54.

M. H. Geoffroy and A. Piétrus, An iterative method for perturbed generalized equations, C. R. Acad. Bulg. Sci. 57 (2004), 7-12.

M. H. Geoffroy and A. Piétrus, A fast iterative scheme for variational inclusions, Discrete Contin. Dyn. Syst., 2009 (2009), 250-258.

F. Giannessi and A. Maugeri, eds., Variational inequalities and network equilibrium problems. Proceedings of a conference, Erice, Italy, June 19-25, 1994., New York, NY: Plenum, 1995. https://doi.org/10.1007/978-1-4899-1358-6

S. Hu and N. S. Papageorgiou, Handbook of multivalued analysis. Volume I: Theory, Dordrecht: Kluwer Academic Publishers, 1997. A. D. Ioffe and V. M. Tihomirov, Theory of extremal problems. Translated from the Russian by K. Makowski, Studies in Mathematics and its Applications, Vol. 6. Amsterdam, New York, Oxford: North-Holland Publishing Company., 1979.

C. Jean-Alexis and A. Piétrus, On the convergence of some methods for variational inclusions, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 102 (2008), 355-361. https://doi.org/10.1007/BF03191828

A. S. Kravchuk and P. J. Neittaanmäki, Variational and quasi-variational inequalities in mechanics, Dordrecht: Springer, 2007. https://doi.org/10.1007/978-1-4020-6377-0

P. S. Macansantos, A generalized Nadler-type theorem in partial metric spaces, Int. Journal of Math. Analysis 7 (2013), 343-348. https://doi.org/10.12988/ijma.2013.13029

P. S. Macansantos, A fixed point theorem for multifunctions in partial metric spaces, J. Nonlinear Anal. Appl. 2013 (2013), 1-7. https://doi.org/10.5899/2013/jnaa-00200

S. G. Matthews, Partial metric topology, in Papers on general topology and applications. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18-20, 1992, New York, NY: The New York Academy of Sciences, 1994, 183-197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x

P. D. Proinov, A generalization of the Banach contraction principle with high order of convergence of successive approximations, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67 (2007), 2361-2369. https://doi.org/10.1016/j.na.2006.09.008

P. D. Proinov, New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems, J. Complexity 26 (2010), 3-42. https://doi.org/10.1016/j.jco.2009.05.001

V. Ptak, Concerning the rate of convergence of Newton's process, Commentat. Math. Univ. Carol. 16 (1975), 699-705.

V. Ptak, The rate of convergence of Newton's process, Numer. Math. 25 (1976), 279-285. https://doi.org/10.1007/BF01399416

M. H. Rashid, J. H. Wang and C. Li, Convergence analysis of a method for variational inclusions, Appl. Anal. 91 (2012), 1943-1956. https://doi.org/10.1080/00036811.2011.618127

S. M. Robinson, Generalized equations and their solutions, part I: basic theory, Math. Program. Study 10 (1979), 128-141. https://doi.org/10.1007/BFb0120850

S. M. Robinson, Generalized equations, in Mathematical Programming The State of the Art, A. Bachem, B. Korte, and M. Gröschel, eds., Springer Berlin Heidelberg, 1983.

S. Romaguera, Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl. 159 (2012), 194-199. https://doi.org/10.1016/j.topol.2011.08.026

I. A. Rus, Generalized contractions and applications, Cluj-Napoca: Cluj University Press, 2001.




How to Cite

A. Benterki, “A local fixed point theorem for set-valued mappings on partial metric spaces”, Appl. Gen. Topol., vol. 17, no. 1, pp. 37–49, Apr. 2016.



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