Title:
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Coincidence and fixed point theorems for nonlinear hybrid generalized contractions (English) |
Author:
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Pathak, H. K. |
Author:
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Kang, S. M. |
Author:
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Cho, Y. J. |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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48 |
Issue:
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2 |
Year:
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1998 |
Pages:
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341-357 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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Weakly commuting |
Keyword:
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compatible and weakly compatible mappings |
Keyword:
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asymptotically regular sequence |
Keyword:
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coincidence point and fixed point |
Keyword:
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Kannan mapping |
MSC:
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47H10 |
MSC:
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54C60 |
MSC:
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54H25 |
idZBL:
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Zbl 0949.54057 |
idMR:
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MR1624260 |
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Date available:
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2009-09-24T10:14:01Z |
Last updated:
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2020-07-03 |
Stable URL:
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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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