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Multivalued \(f\)-weakly Picard mappings. (English) Zbl 1128.54024

By introducing the concept of multi-valued \(f\)-weak contraction and generalized multi-valued \(f\)-weak contraction, the author obtains two coincidence fixed point theorems which include, in particular, two common fixed point theorems. If \(f=I\), the identity map, one obtains the results co-authored by the reviewer: M. Berinde and V. Berinde [J. Math. Anal. Appl. 326, 772–782 (2007; Zbl 1117.47039)].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems

Citations:

Zbl 1117.47039
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References:

[1] Assad, N. A.; Kirk, W. A., Fixed point theorems for setvalued mappings of contractive type, Pacific J. Math., 43, 553-562 (1972) · Zbl 0239.54032
[2] Berinde, V., Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9, 1, 43-53 (2004) · Zbl 1078.47042
[3] Berinde, V., Generalized Contractions and Applications, vol. 22 (1997), Cub Press: Cub Press Baia Mare, (in Romanian)
[4] V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002; V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002
[5] Berinde, V., On approximation of fixed points of weak \(\phi \)-contractive operators, Fixed Point Theory, 4, 131-142 (2003)
[6] M. Berinde, V. Berinde, On general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. (in press); M. Berinde, V. Berinde, On general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. (in press) · Zbl 1117.47039
[7] Chatterjea, S. K., Fixed point theorems, C. R. Acad. Bulgare Sci., 25, 727-730 (1972) · Zbl 0274.54033
[8] Ciric, Lj. B., Fixed point theory, (Contraction Mapping Principle (2003), FME Press: FME Press Beograd) · Zbl 1122.47044
[9] Daffer, P. Z.; Kaneko, H., Fixed points of generalized contractive multivalued mappings, J. Math. Anal. Appl., 192, 655-666 (1995) · Zbl 0835.54028
[10] Dugundji, J.; Granas, A., Weakly contractive maps and elementary domain invariance theorem, Bull. Greek Math. Soc., 19, 141-151 (1978) · Zbl 0417.54010
[11] Kamran, T., Coincidence and fixed points for hybrid strict contractions, J. Math. Anal. Appl., 299, 235-241 (2004) · Zbl 1064.54055
[12] Kamran, T., Fixed points of asymptotically regular noncompatible maps, Demonstratio Math., XXXVIII, 485-494 (2005) · Zbl 1070.54020
[13] Mizoguchi, N.; Takahashi, W., Fixed point theorems for multivalued mappings on complete metric space, J. Math. Anal. Appl., 141, 177-188 (1989) · Zbl 0688.54028
[14] Nadler, S. B., Multivalued contraction mappings, Pacific J. Math., 30, 475-488 (1969) · Zbl 0187.45002
[15] Pant, R. P., Common fixed points of non-commuting mappings, J. Math. Anal. Appl., 188, 436-440 (1994) · Zbl 0830.54031
[16] Pant, R. P., Common fixed point theorems for contractive maps, J. Math. Anal. Appl., 226, 251-258 (1998) · Zbl 0916.54027
[17] Pathak, H. K.; Khan, M. S., Fixed and coincidence points of hybrid mappings, Arch. Math. (Brno), 38, 201-208 (2002) · Zbl 1068.47073
[18] Petrusel, A., On Frigon-Granas-type multifunctions, Nonlinear Anal. Forum, 7, 113-121 (2002) · Zbl 1043.47036
[19] Reich, S., Kannan’s fixed point theorem, Boll. Unione Mat. Ital., 4, 1-11 (1971) · Zbl 0219.54042
[20] Reich, S., A fixed point theorem for locally contractive multi-valued functions, Rev. Roumaine Math. Pures Appl., 17, 569-572 (1972) · Zbl 0239.54033
[21] Reich, S., Fixed points of contractive functions, Boll. Unione Mat. Ital., 5, 26-42 (1972) · Zbl 0249.54026
[22] Reich, S., Some problems and results in fixed point theory, Contemp. Math., 21, 179-187 (1983) · Zbl 0531.47048
[23] Rus, I. A., Generalized Contractions and Applications (2001), Cluj University Press: Cluj University Press Cluj-Napoca · Zbl 0968.54029
[24] Rus, I. A.; Petrusel, A.; Sintamarian, A., Data dependence of fixed point set of some multi-valued weakly Picard operators, Nonlinear Anal., 52, 1947-1959 (2003) · Zbl 1055.47047
[25] Sintamarian, A., Some pairs of multi-valued operators, Carpathian J. Math., 21, 115-125 (2005) · Zbl 1101.47032
[26] Shahzad, N., Invariant approximation and \(R\)-subweakly commuting maps, J. Math. Anal. Appl., 257, 39-45 (2001) · Zbl 0989.47047
[27] Shahzad, N., Coincidence points and \(R\)-subweakly commuting multivalued maps, Demonstratio Math., 36, 427-431 (2003) · Zbl 1039.54023
[28] Singh, S. L.; Mishra, S. N., Coincidence and fixed points of nonself hybrid contractions, J. Math. Anal. Appl., 256, 486-497 (2001) · Zbl 0985.47046
[29] Zamfirescu, T., Fix point theorems in metric spaces, Arch. Math. (Basel), 23, 292-298 (1972) · Zbl 0239.54030
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