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Khojasteh, Farshid; Abbas, Mujahid; Costache, Simona

Two new types of fixed point theorems in complete metric spaces. (English) Zbl 1436.54035

Abstr. Appl. Anal. 2014, Article ID 325840, 5 p. (2014).
Summary: We introduce two new types of fixed point theorems in the collection of multivalued and single-valued mappings in complete metric spaces.

Cited in 8 Reviews
Cited in 11 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
54C60 Set-valued maps in general topology

Keywords:

fixed point theorem; multivalued map; single-valued map; complete metric space
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References:

[1] Leader, S., Equivalent Cauchy sequences and contractive fixed points in metric spaces, Studia Mathematica, 76, 1, 63-67 (1983) · Zbl 0469.54028
[2] Rus, I. A., Picard operators and applications, Scientiae Mathematicae, 58, 1, 191-219 (2003) · Zbl 1031.47035
[3] Subrahmanyam, P. V., Remarks on some fixed point theorems related to Banach’s contraction principle, Journal of Mathematical and Physical Sciences, 8, 445-457 (1974) · Zbl 0294.54033
[4] Rus, I. A.; Muresan, A. S.; Muresan, V., Weakly Picard operators on a set with two metrics, Fixed Point Theory, 6, 2, 323-331 (2005) · Zbl 1112.47306
[5] Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions, Transactions of the American Mathematical Society, 215, 241-251 (1976) · Zbl 0305.47029 · doi:10.1090/S0002-9947-1976-0394329-4
[6] Caristi, J.; Kirk, W. A., Geometric fixed point theory and inwardness conditions, The Geometry of Metric and Linear Spaces. The Geometry of Metric and Linear Spaces, Lecture Notes in Mathematics, 490, 74-83 (1975), Berlin, Germany: Springer, Berlin, Germany · Zbl 0315.54052 · doi:10.1007/BFb0081133
[7] Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae, 3, 133-181 (1922) · JFM 48.0201.01
[8] Ćirić, L. B., A generalization of Banach’s contraction principle, Proceedings of the American Mathematical Society, 45, 267-273 (1974) · Zbl 0291.54056
[9] Kannan, R., Some results on fixed points—II, The American Mathematical Monthly, 76, 4, 405-408 (1969) · Zbl 0179.28203 · doi:10.2307/2316437
[10] Kirk, W. A., Fixed points of asymptotic contractions, Journal of Mathematical Analysis and Applications, 277, 2, 645-650 (2003) · Zbl 1022.47036 · doi:10.1016/S0022-247X(02)00612-1
[11] Matkowski, J., Integrable solutions of functional equations, Dissertationes Mathematicae, 127, 1-68 (1975) · Zbl 0318.39005
[12] Meir, A.; Keeler, E., A theorem on contraction mappings, Journal of Mathematical Analysis and Applications, 28, 326-329 (1969) · Zbl 0194.44904 · doi:10.1016/0022-247X(69)90031-6
[13] Suzuki, T., Generalized distance and existence theorems in complete metric spaces, Journal of Mathematical Analysis and Applications, 253, 2, 440-458 (2001) · Zbl 0983.54034 · doi:10.1006/jmaa.2000.7151
[14] Suzuki, T., Several fixed point theorems concerning \(\tau \)-distance, Fixed Point Theory and Applications, 2004, 3, 195-209 (2004) · Zbl 1076.54532 · doi:10.1155/S168718200431003X
[15] Suzuki, T., A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point, Proceedings of the American Mathematical Society, 136, 11, 4089-4093 (2008) · Zbl 1152.54033 · doi:10.1090/S0002-9939-08-09390-8
[16] Bae, J. S., Fixed point theorems for weakly contractive multivalued maps, Journal of Mathematical Analysis and Applications, 284, 2, 690-697 (2003) · Zbl 1033.47038 · doi:10.1016/S0022-247X(03)00387-1
[17] Bae, J. S.; Cho, E. W.; Yeom, S. H., A generalization of the Caristi-Kirk fixed point theorem and its applications to mapping theorems, Journal of the Korean Mathematical Society, 31, 1, 29-48 (1994) · Zbl 0842.47035
[18] Kirk, W. A.; Kirk, W. A.; Sims, B., Contraction mappings and extensions, Handbook of Metric Fixed Point Theory, 1-34 (2001), Dordrecht, The Netherlands: Kluwer Academic, Dordrecht, The Netherlands · Zbl 1019.54001
[19] Aydi, H.; Shatanawi, W.; Postolache, M.; Mustafa, Z.; Tahat, N., Theorems for Boyd-Wong-type contractions in ordered metric spaces, Abstract and Applied Analysis, 2012 (2012) · Zbl 1253.54036 · doi:10.1155/2012/359054
[20] Chandok, S.; Postolache, M., Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed Point Theory and Applications, 2013, 28 (2013) · Zbl 1300.54060 · doi:10.1186/1687-1812-2013-28
[21] Chandok, S.; Mustafa, Z.; Postolache, M., Coupled common fixed point results for mixed \(g\)-monotone mapps in partially ordered \(G\)-metric spaces, University Politehnica of Bucharest Scientific Bulletin A, 75, 4, 13-26 (2013) · Zbl 1299.41058
[22] Chen, Y., Stability of positive fixed points of nonlinear operators, Positivity, 6, 1, 47-57 (2002) · Zbl 1008.47048 · doi:10.1023/A:1012079817987
[23] Choudhury, B. S.; Metiya, N.; Postolache, M., A generalized weak contraction principle with applications to coupled coincidence point problems, Fixed Point Theory and Applications, 2013, article 152 (2013) · Zbl 1295.54050 · doi:10.1186/1687-1812-2013-152
[24] Haghi, R. H.; Postolache, M.; Rezapour, S., On T-stability of the Picard iteration for generalized \(\varphi \)-contraction mappings, Abstract and Applied Analysis, 2012 (2012) · Zbl 1252.54035 · doi:10.1155/2012/658971
[25] Ilić, D.; Rakočević, V., Common fixed points for maps on cone metric space, Journal of Mathematical Analysis and Applications, 341, 2, 876-882 (2008) · Zbl 1156.54023 · doi:10.1016/j.jmaa.2007.10.065
[26] Jachymski, J., The contraction principle for mappings on a metric space with a graph, Proceedings of the American Mathematical Society, 136, 4, 1359-1373 (2008) · Zbl 1139.47040 · doi:10.1090/S0002-9939-07-09110-1
[27] Lakshmikantham, V.; Ćirić, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 70, 12, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[28] Nieto, J. J.; Pouso, R. L.; Rodriguez-Lopez, R., Fixed point theorems in ordered abstract spaces, Proceedings of the American Mathematical Society, 135, 8, 2505-2517 (2007) · Zbl 1126.47045 · doi:10.1090/S0002-9939-07-08729-1
[29] Nieto, J. J.; Rodriguez-Lopez, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 3, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[30] Nieto, J. J.; Rodríguez-López, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Mathematica Sinica, 23, 12, 2205-2212 (2007) · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[31] O’Regan, D.; Petruşel, A., Fixed point theorems for generalized contractions in ordered metric spaces, Journal of Mathematical Analysis and Applications, 341, 2, 1241-1252 (2008) · Zbl 1142.47033 · doi:10.1016/j.jmaa.2007.11.026
[32] Pathak, H. K.; Shahzad, N., Fixed points for generalized contractions and applications to control theory, Nonlinear Analysis. Theory, Methods & Applications, 68, 8, 2181-2193 (2008) · Zbl 1144.54031 · doi:10.1016/j.na.2007.01.041
[33] Shatanawi, W.; Postolache, M., Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory and Applications, 2013, article 271 (2013) · Zbl 1297.54102 · doi:10.1186/1687-1812-2013-271
[34] Shatanawi, W.; Postolache, M., Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, Fixed Point Theory and Applications, 2013, 60 (2013) · Zbl 1286.54053 · doi:10.1186/1687-1812-2013-60
[35] Wu, Y., New fixed point theorems and applications of mixed monotone operator, Journal of Mathematical Analysis and Applications, 341, 2, 883-893 (2008) · Zbl 1137.47044 · doi:10.1016/j.jmaa.2007.10.063
[36] Nadler, J., Multi-valued contraction mappings, Pacific Journal of Mathematics, 30, 475-488 (1969) · Zbl 0187.45002 · doi:10.2140/pjm.1969.30.475
[37] Amini-Harandi, A., Endpoints of set-valued contractions in metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 72, 1, 132-134 (2010) · Zbl 1226.54042 · doi:10.1016/j.na.2009.06.074
[38] Amini-Harandi, A., Fixed point theory for set-valued quasi-contraction maps in metric spaces, Applied Mathematics Letters, 24, 11, 1791-1794 (2011) · Zbl 1230.54034 · doi:10.1016/j.aml.2011.04.033
[39] Ciric, L. B.; Ume, J. S., Multi-valued non-self-mappings on convex metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 60, 6, 1053-1063 (2005) · Zbl 1078.47015 · doi:10.1016/j.na.2004.09.057
[40] Fakhar, M., Endpoints of set-valued asymptotic contractions in metric spaces, Applied Mathematics Letters, 24, 4, 428-431 (2011) · Zbl 1206.54043 · doi:10.1016/j.aml.2010.10.028
[41] Hussain, N.; Amini-Harandi, A.; Cho, Y. J., Approximate endpoints for set-valued contractions in metric spaces, Fixed Point Theory and Applications, 2010 (2010) · Zbl 1202.54033 · doi:10.1155/2010/614867
[42] Kadelburg, Z.; Radenović, S., Some results on set-valued contractions in abstract metric spaces, Computers & Mathematics with Applications, 62, 1, 342-350 (2011) · Zbl 1228.54041 · doi:10.1016/j.camwa.2011.05.015
[43] Moradi, S.; Khojasteh, F., Endpoints of multi-valued generalized weak contraction mappings, Nonlinear Analysis: Theory, Methods & Applications, 74, 6, 2170-2174 (2011) · Zbl 1296.54077 · doi:10.1016/j.na.2010.11.021
[44] Khojasteh, F.; Rakočević V., Some new common fixed point results for generalized contractive multi-valued non-self-mappings, Applied Mathematics Letters, 25, 3, 287-293 (2012) · Zbl 1242.54024 · doi:10.1016/j.aml.2011.07.021
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