Multi-valued operators with respect $wt$-distance on metric type spaces

Document Type : Research Paper

Authors

1 Universita degli Studi di Palermo‎, ‎Dipartimento di Matematica e Informatica‎, ‎Via Archirafi‎, ‎34‎, ‎90123 Palermo‎, ‎Italy.

2 Department of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Tehran‎, ‎Iran.

3 Universita degli Studi di Palermo‎, ‎Dipartimento di Matematica e nformatica‎, ‎Via Archirafi‎, ‎34‎, ‎90123 Palermo‎, ‎Italy.

Abstract

‎Recently‎, ‎Hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎In this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎These results generalize a result of Feng and Liu on multi-valued operators.

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References

R. P. Agarwal, N. Hussain and M.-A. Taoudi, Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations, Abstr. Appl. Anal. 2012 (2012), Article ID 245872, 15 pages.
M. A. Alghamdi, N. Hussain and P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl. 2013 (2013), no. 402, 25 pages.
I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989) 26--37.
S. Banach, Sur les operations dans les ensembles abstraits et leur application auxequations integrales, Fund. Math. 3 (1922) 133--181.
M. Boriceanu, A. Petrusel and I. A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Int. J. Math. Stat. 6 (2010), S10, 65--76.
M. Bota, A. Molnar and C. Varga, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory 12 (2011), no. 1, 21--28.
C. Chifu and G. Petrusel, Existence and data dependence of fixed points and strict fixed points for contractive-type multivalued operators, Fixed Point Theory Appl. 2007 (2007), Article ID 34248, 8 pages.
Y. J. Cho, R. Saadati and S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011), no. 4, 1254--1260.
M. Cosentino, M. Jleli, B. Samet and C. Vetro, Solvability of integrodifferential problems via fixed point theory in b-metric spaces, Fixed Point Theory Appl. 2015 (2015), no. 70, 15 pages.
M. Cosentino, P. Salimi and P. Vetro, Fixed point results on metric-type spaces, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 4, 1237--1253.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis 1 (1993) 5--11.
Y. Feng and S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappinggs, J. Math. Anal. Appl. 371 (2006), no. 1, 103--112.
E. Graily, S. M. Vaezpour, R. Saadati and Y. J. Cho, Generalization of fixed point theorems in ordered metric spaces concerning generalized distance, Fixed Point Theory Appl. 2011 (2011), no. 30, 8 pages.
L. Guran, Fixed points for multivalued operators with respect to a w-distance on metric spaces, Carpathian J. Math. 23 (2007), no. 1-2, 89--92.
N. Hussain, D. Doric, Z. Kadelburg and S. Radenovic, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl. 2012 (2012), no. 126, 12 pages.
N. Hussain, P. Salimi and V. Parvaneh, Fixed point results for various contractions in parametric and fuzzy b-metric spaces, J. Nonlinear Sci. Appl. 8 (2015), no. 5, 719--739.
N. Hussain, R. Saadati and R. P. Agrawal, On the topology and wt-distance on metric type spaces, Fixed Point Theory Appl. 2014 (2014), no. 88, 14 pages.
N. Hussain and M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011), no. 4, 1677--1684.
D. Ilic, V. Rakocevic, Common fixed points for maps on metric space with w-distance, Comput. Math. Appl. 199 (2008), no. 2, 599--610.
M. B. Jleli, B. Samet, C. Vetro and F. Vetro, Fixed points for multivalued mappings in b-metric spaces, Abstr. Appl. Anal. 2015 (2015), Article ID 718074, 7 pages.
M. Jovanovic, Z. Kadelburg and S. Radenovic, Common fixed point results in metric type spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 978121, 7 pages.
O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Sci. Math. Jpn. 44 (1996), no. 2, 381--391.
Z. Kadelburg and S. Radenovic, Pata-type common fixed point results in b-metric and b-rectangular metric spaces, J. Nonlinear Sci. Appl. 8 (2015), no. 6, 944--954.
M. A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 315398, 7 pages.
M. A. Khamsi and N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal. 73 (2010), no. 9, 3123--3129.
V. La Rosa and P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl. 7 (2014), no. 1, 1--10.
S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475--488. D. Reem, S. Reich and A. J. Zaslavski, Two Results in Metric Fixed Point Theory, J. Fixed Point Theory Appl. 1 (2007), no. 1, 149--157.
S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. (4) 5 (1972) 26--42.
S. Reich and A. J. Zaslavski, A fixed point theorem for Matkowski contractions, Fixed Point Theory 8 (2007), no. 2, 303--307.
S. Reich and A. J. Zaslavski, A note on Rakotch contraction, Fixed Point Theory 9 (2008), no. 1, 267--273.
M. H. Shah, S. Simic, N. Hussain, A. Sretenovic and S. Radenovi_c, Common fixed points theorems for occasionally weakly compatible pairs on cone metric type spaces, J. Comput. Anal. Appl. 14 (2012), no. 2, 290--297.
W. Sintunavarat, Y. J. Cho and P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. 62 (2011) 1969--1978.
T. Suzuki and W. Takahashi, Fixed points theorems and characterizations of metric completeness, Topol. Methods Nonlinear Anal. 8 (1996) 371--382.
C. Vetro and F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. 6 (2013) no. 3, 152--161.
Bulletin of the Iranian Mathematical Society
Volume 42, Issue 6
December 2016
Pages 1571-1582

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History

  • Receive Date: 09 February 2015
  • Revise Date: 03 October 2015
  • Accept Date: 03 October 2015

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