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Title: Coincidence and fixed point theorems for nonlinear hybrid generalized contractions (English)
Author: Pathak, H. K.
Author: Kang, S. M.
Author: Cho, Y. J.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 48
Issue: 2
Year: 1998
Pages: 341-357
Summary lang: English
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Category: math
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Summary: In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors. (English)
Keyword: Weakly commuting
Keyword: compatible and weakly compatible mappings
Keyword: asymptotically regular sequence
Keyword: coincidence point and fixed point
Keyword: Kannan mapping
MSC: 47H10
MSC: 54C60
MSC: 54H25
idZBL: Zbl 0949.54057
idMR: MR1624260
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Date available: 2009-09-24T10:14:01Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/127421
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Reference: [1] I. Beg and A. Azam: Fixed point theorems for Kannan mappings.Indian J. Pure and Appl. Math. 17(11) (1986), 1270–1275. MR 0868963
Reference: [2] I. Beg and A. Azam: Fixed points of asymptotically regular multivalued mappings.J. Austral. Math. Soc. (Series A) 53 (1992), 313–326. MR 1187851, 10.1017/S1446788700036491
Reference: [3] K. M. Das and K. V. Naik: Common fixed point theorems for commuting maps on a metric space.Proc. Amer. Math. Soc. 77 (1979), 369–373. MR 0545598
Reference: [4] B. Fisher: Common fixed points of four mappings.Bull. Inst. Math. Acad. Sinica 11 (1983), 103–113. Zbl 0515.54029, MR 0718906
Reference: [5] G.Jungck: Commuting mappings and fixed points.Amer. Math. Monthly 83 (1976), 261-163. Zbl 0321.54025, MR 0400196, 10.2307/2318216
Reference: [6] G.Jungck: Compatible mappings and common fixed points.Internat. J. Math. & Math. Sci. 9 (1986), 771–779. MR 0870534, 10.1155/S0161171286000935
Reference: [7] G.Jungck: Common fixed points for commuting and compatible maps on compacta.Proc. Amer. Math. Soc. 103 (1988), 997–983. Zbl 0661.54043, MR 0947693
Reference: [8] H. Kaneko: Single-valued and multi-valued f-contractions.Boll. Un. Mat. Ital. 4-A (1985), 29–33. Zbl 0568.54031, MR 0781791
Reference: [9] H. Kaneko: A common fixed point of weakly commuting multi-valued mappings.Math. Japonica 33(5) (1988), 741–744. MR 0972386
Reference: [10] H. Kaneko and S. Sessa: Fixed point theorem for compatible multi-valued and single-valued mappings.Internat. J. Math. & Math. Sci. 12 (1989), 257–262. MR 0994907, 10.1155/S0161171289000293
Reference: [11] R. Kannan: Some results on fixed points.Bull. Calcutta. Math. Soc. 60 (1968), 71–76. Zbl 0209.27104, MR 0257837
Reference: [12] R. Kannan: Fixed point theorem in reflexive Banach spaces.Proc. Amer. Math. Soc. 38 (1973), 111–118. MR 0313896, 10.1090/S0002-9939-1973-0313896-2
Reference: [13] T. Kubiak: Fixed point theorems for contractive type multi-valued mappings.Math. Japonica 30 (1985), 89–101. MR 0828906
Reference: [14] H. K. Pathak: On a fixed point theorem of Jungck.to appear in Proceedings of the First World Congress of Nonlinear Analyst, 1992. MR 1389316
Reference: [15] H. K. Pathak: On common fixed points of weak compatible mappings in metric and Banach spaces.to appear in Nonlinear Functional Analysis and its Applications, special volume (Ed. T. M. Rassias) (1993).
Reference: [16] H. K. Pathak: Fixed point theorem for weak compatible multi-valued and single-valued mappings.Acta. Math. Hungar. 67(1–2) (1995), 69–78. MR 1316710, 10.1007/BF01874520
Reference: [17] H. K. Pathak and V. Popa: On common fixed points of weak compatible mappings in metric spaces.Studii Si Ćercetǎri Stiintifice, Seria: Mathematicǎ 3 (1994), 89–100. MR 1434745
Reference: [18] H. K. Pathak and V. Popa: Common fixed points of weak compatible mappings.Studia Univ. Babes-Bolyai Mathematica 34(1) (1994), 65–78. MR 1434745
Reference: [19] S. Nadler: Multi-valued contraction mappings.Pacific J. Math. 20 (1969), 475–488. Zbl 0187.45002, MR 0254828, 10.2140/pjm.1969.30.475
Reference: [20] B. E. Rhoades, S. Sessa, M. S. Khan and M. Swaleh: On fixed points of asymptotically regular mappings.J. Austral. Math. Soc. (Series A) 43 (1987), 328–346. MR 0904393, 10.1017/S1446788700029621
Reference: [21] S. Sessa: On a weak commutativity condition of mappings in fixed point considerations.Publ. Inst. Math. (Beograd) 32(46) (1982), 146–153. Zbl 0523.54030, MR 0710984
Reference: [22] C. Shiau, K. K. Tan and C. S. Wong: A class of quasi-nonexpansive multi-valued maps.Canad. Math. Bull. 18 (1975), 707–714. MR 0407667, 10.4153/CMB-1975-124-2
Reference: [23] S. L. Singh and S. P. Singh: A fixed point theorem.Indian J. Pure and Appl. Math. 11 (1980), 1584–1586. MR 0617835
Reference: [24] S. L. Singh, K. S. Ha and Y. J. Cho: Coincidence and fixed points of nonlinear hybrid contractions.Internat. J. Math. & Math. Sci. 12(2) (1989), 247–256. MR 0994906, 10.1155/S0161171289000281
Reference: [25] R. E. Smithson: Fixed points for contractive multi-functions.Proc. Amer. Math. Soc. 27 (1971), 192–194. MR 0267564, 10.1090/S0002-9939-1971-0267564-4
Reference: [26] C. S. Wong: On Kannan maps.Proc. Amer. Math. Soc. 47 (1975), 105–111. MR 0358468, 10.1090/S0002-9939-1975-0358468-0
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