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Common fixed points of generalized contractions on partial metric spaces and an application. (English) Zbl 1244.54090
The authors develop the fixed point theory on partial metric spaces and give some common fixed point theorems for four mappings satisfying the Ćirić type contraction condition. The main result (Theorem 2.1) generalizes the one proved quite recently in [I. Altun, F. Sola and H. Simsek, Topology Appl. 157, No. 18, 2778–2785 (2010); corrigendum ibid. 158, No. 13, 1738–1740 (2011; Zbl 1207.54052)]. At the end of the paper some homotopy results are presented. Under suitable assumptions on a homotopy H (contractivity and continuity type conditions) the authors prove that H(·,0) has a fixed point iff H(·,1) has a fixed point.
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
References:
[1]Altman, M.: An integral test for series and generalized contractions, Am. math. Mon. 82, 827-829 (1975) · Zbl 0326.40001 · doi:10.2307/2319801
[2]Altun, I.; Sola, F.; Simsek, H.: Generalized contractions on partial metric spaces, Topol. appl. 157, No. 18, 2778-2785 (2010) · Zbl 1207.54052 · doi:10.1016/j.topol.2010.08.017
[3]Babu, G. V. R.; Prasad, K. N. V.V. Vara: Common fixed point theorems of different compatible type mappings using Ćirić’s contraction type condition, Math. commun. 11, 87-102 (2006) · Zbl 1120.47045
[4]Berinde, V.: Some remarks on a fixed point theorem for ciric-type almost contractions, Carpathian J. Math. 25, No. 2, 157-162 (2009)
[5]&cacute, Lj. B.; Irić: Generalized contractions and fixed point theorems, Publ. inst. Math. 12, 19-26 (1971)
[6]Heckmann, R.: Approximation of metric spaces by partial metric spaces, Appl. categ. Struct. 7, 71-83 (1999) · Zbl 0993.54029 · doi:10.1023/A:1008684018933
[7]Jungck, G.; Rhoades, B. E.: Fixed points for set valued functions without continiuty, Indian. J. Pur. appl. Math. 29, 227-238 (1998) · Zbl 0904.54034
[8]S.G. Matthews, Partial metric topology, in: Proceedings Eighth Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci. 728 (1994) 183 – 197.
[9]Oltra, S.; Valero, O.: Banach’s fixed point theorem for partial metric spaces, Rend. istit. Mat. univ. Trieste. 36, 17-26 (2004) · Zbl 1080.54030
[10]S.J. O’ Neill, Partial metrics, valuations and domain theory, in: Proceedings Eleventh Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci. 806 (1996) 304 – 315. · Zbl 0889.54018
[11]Ray, B. K.: On Ćirić’s fixed point theorem, Fund. math. 94, No. 3, 221-229 (1977)
[12]Rhoades, B. E.: A comparison of various definitions of contractive mappings, Trans. amer. Math. soc. 226, 257-290 (1977) · Zbl 0365.54023 · doi:10.2307/1997954
[13]S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theor. Appl. (2010), Article ID 493298, 6 pages. · Zbl 1193.54047 · doi:10.1155/2010/493298
[14]Romaguera, S.; Schellekens, M.: Partial metric monoids and semivaluation spaces, Topol. appl. 153, No. 5-6, 948-962 (2005) · Zbl 1084.22002 · doi:10.1016/j.topol.2005.01.023
[15]Romaguera, S.; Valero, O.: A quantitative computational model for complete partial metric spaces via formal balls, Math. struct. Comput. sci. 19, No. 3, 541-563 (2009) · Zbl 1172.06003 · doi:10.1017/S0960129509007671
[16]Schellekens, M. P.: The correspondence between partial metrics and semivaluations, Theoret. comput. Sci. 315, 135-149 (2004) · Zbl 1052.54026 · doi:10.1016/j.tcs.2003.11.016
[17]Singh, S. L.; Mishra, S. N.: On a ljubomir Ćirić’s fixed point theorem for nonexpansive type maps with applications, Indian J. Pure appl. Math. 33, 531-542 (2002)
[18]Valero, O.: On Banach fixed point theorems for partial metric spaces, Appl. gen. Topol. 6, No. 2, 229-240 (2005) · Zbl 1087.54020
[19]Waszkiewicz, P.: Partial metrisability of continuous posets, Math. struct. Comput. sci. 16, No. 2, 359-372 (2006) · Zbl 1103.06004 · doi:10.1017/S0960129506005196