Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

[1] M. Abbas, Lj. Ćirić, B. Damjanović, M.A. Khan, Coupled coincidence and common fixed point theorems for hybrid pair of mappings, Fixed Point Theory Appl. 2012 (4)(2012) 11 pages.10.1186/1687-1812-2012-4Search in Google Scholar

[2] A. Amini Harandi, Fixed point theory for set-valued quasi-contraction maps in metric spaces, Appl. Math. Lett. 24 (2011) 1791–1794.10.1016/j.aml.2011.04.033Search in Google Scholar

[3] T.V. An, N.V Dung, Z. Kadelburg, S. Radenović, Various generalizations of metric spaces and fixed point theorems, RACSAM 109 (2015) 175–198.10.1007/s13398-014-0173-7Search in Google Scholar

[4] T.V. An, L.Q. Tuyen, N.V. Dung, Stone-type theorem on b-metric spaces and applications, Topology Appl. 185-186 (2015) 50–64.10.1016/j.topol.2015.02.005Search in Google Scholar

[5] T.V. An, N.V Dung, Answers to Kirk-Shahzad’s questions on strong b-metric spaces, Taiwanese J. Math. 20 (5) (2016) 1175–1184.10.11650/tjm.20.2016.6359Search in Google Scholar

[6] H. Aydi, M.F. Bota, E. Karapınar, S. Mitrović, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl. 2012 (88)(2012) 8 pages.10.1186/1687-1812-2012-88Search in Google Scholar

[7] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fundam. Math. 3 (1922) 133–181.10.4064/fm-3-1-133-181Search in Google Scholar

[8] C. Berge, Espaces topologiques-Fonctions multivoques, Dunod, Paris, (1966).Search in Google Scholar

[9] M. Boriceanu, A. Petruşel, I.A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Internat. J. Math. Statistics 6 (2010) 65–76.Search in Google Scholar

[10] M. Boriceanu, M. Bota, A. Petruşel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math. 8 (2)(2010) 367–377.10.2478/s11533-010-0009-4Search in Google Scholar

[11] S. Cobzaş, Fixed points and completeness in metric and in generalized metric spaces, arXiv preprint arXiv: 1508.05173 (2016) 71 pages.Search in Google Scholar

[12] Lj. Ćirić, A generalization of Banach contraction principle, Proc. Am. Math. Soc., 45 (1974) 267–273.10.1090/S0002-9939-1974-0356011-2Search in Google Scholar

[13] Lj. Ćirić, M. Abbas, M. Rajović, B. Ali, Suzuki type fixed point theorems for generalized multivalued mappings on a set endowed with two b-metric, Appl. Math. Comput., 219 (2012) 1712–1723.10.1016/j.amc.2012.08.011Search in Google Scholar

[14] C. Chifu, G. Petruşel, Fixed points for multivalued contractions in b-metric spaces with applications to fractals, Taiwan. J. Math., 18 (5)(2014) 1365–1375.10.11650/tjm.18.2014.4137Search in Google Scholar

[15] E.H. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc., 10 (1959) 974–979.10.1090/S0002-9939-1959-0110093-3Search in Google Scholar

[16] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993) 5–11.Search in Google Scholar

[17] S. Czerwik, K. Dlutek, S.L. Singh, Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci. 11 (1997) 87–94.Search in Google Scholar

[18] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena, 46 (1998) 263–276.Search in Google Scholar

[19] N. Van Dung, V.T. Le Hang, On relaxations of contraction constants and Caristi’s theorem in b-metric spaces, J. Fixed Point Theory Appl., 18 (2) (2016) 267–284.10.1007/s11784-015-0273-9Search in Google Scholar

[20] M. Elekes, On a converse to Banach’s fixed point theorem, Proc. Amer. Math. Soc. 137 (9) (2009) 3139–3146.10.1090/S0002-9939-09-09904-3Search in Google Scholar

[21] R.H. Haghi, Sh. Rezapour, N. Shahzad, Some fixed point generalisations are not real generalizations, Nonlinear Anal. 74 (2011) 1799–1803.10.1016/j.na.2010.10.052Search in Google Scholar

[22] N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed point theory Appl. 2012 (126)(2012) 12 pages.10.1186/1687-1812-2012-126Search in Google Scholar

[23] M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric type spaces, Fixed Point Theory Appl. 2010 (2010) 15 pages.10.1155/2010/204981Search in Google Scholar

[24] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968) 71–76.10.2307/2316437Search in Google Scholar

[25] R. Kannan, Some results on fixed points II, Amer. Math. Monthly 76 (1969) 405–408.10.1080/00029890.1969.12000228Search in Google Scholar

[26] W.A. Kirk, N. Shahzad, Fixed point theory in distance spaces, Springer, Cham (2014).10.1007/978-3-319-10927-5Search in Google Scholar

[27] M. Kikkawa, T. Suzuki, Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl. 2008 (2008) 8 pages.10.1155/2008/649749Search in Google Scholar

[28] M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008) 2942–2949.10.1016/j.na.2007.08.064Search in Google Scholar

[29] M.A. Kutbi, E. Karapinar, J. Ahmad, A. Azam, Some fixed point results for multivalued mappings in b-metric spaces, J. Inequal. Appl. 2014 (126)(2014) 11 pages.10.1186/1029-242X-2014-126Search in Google Scholar

[30] T.C. Lim, Fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985) 436–441.10.1016/0022-247X(85)90306-3Search in Google Scholar

[31] S.B. Nadler Jr., multivalued contraction mappings, Pac. J. Math. 30 (1969) 475–488.10.2140/pjm.1969.30.475Search in Google Scholar

[32] S. Park, B. E. Rhoades, Comments on characterizations for metric completeness, Math. Japon. 31 (1)(1986) 95–97.Search in Google Scholar

[33] S. Reich, Fixed Points of contractive functions, Boll. Unione Mat. Ital. 5 (1972) 26–42.Search in Google Scholar

[34] I.A. Rus, A. Petruşel, A. Sîntăamăarian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947–1959.10.1016/S0362-546X(02)00288-2Search in Google Scholar

[35] S.L. Singh, B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl. 55 (2008) 2512–2520.10.1016/j.camwa.2007.10.026Search in Google Scholar

[36] S.L. Singh, S. Czerwik, K. Krol, A. Singh, Coincidences and fixed points of hybrid contractions, Tamsui Oxford Univ. J. Math. Sci. 24 (2008) 401–416.Search in Google Scholar

[37] S.L. Singh, S.N. Mishra, W. Sinkala, A note on fixed point stability for generalized set-valued contractions, Appl. Math. Lett. 25 (2012) 1708–1710.10.1016/j.aml.2012.01.042Search in Google Scholar

[38] P.V. Subrahmanyam, Completeness and fixed-points, Monatsh. Math. 80 (1975) 325–330.10.1007/BF01472580Search in Google Scholar

[39] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (5)(2008) 1861–1869.10.1090/S0002-9939-07-09055-7Search in Google Scholar