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On two pairs of non-self hybrid mappings

Part of: Nonlinear operators and their properties Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

Ljubomir B. Ćirić ,
Jeong Sheok Ume  and
Nebqjša T. Nikolić
Ljubomir B. Ćirić
Affiliation:
Faculty of Mechanical EngineeringAl. Rudara 12-35 11 070 Belgrade Serbia and Montenegrolciric@afrodita.rcub.bg.ac.yu
Jeong Sheok Ume
Affiliation:
Department of Applied MathematicsChangwon National UniversityChangwon 641-773 Koreajsume@changwon.ac.kr
Nebqjša T. Nikolić
Affiliation:
Faculty of Organizational ScienceJove Ilica 154 11 000 Belgrade Serbiasigma@fon.bg.ac.yu
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Abstract

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Abstrac In this paper we obtain some results on coincidence and common fixed points for two pairs of multi-valued and single-valued non-self mappings in complete convex metric spaces. We improve on previously used methods of proof and obtain results for mappings which are not necessarily compatible and not necessarily continuous, generalizing some known results. In particular, a theorem by Rhoades [19] and a theorem by Ahmed and Rhoades [2] are generalized and improved.

MSC classification

Secondary: 54H25: Fixed-point and coincidence theorems 47H10: Fixed-point theorems

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 1 , August 2007 , pp. 17 - 30
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Ahmed, A. and Khan, A. R., ‘Some fixed point theorems for non-self hybird contractions’, J. Math. Anal. Appl. 213 (1997), 275–280.CrossRefGoogle Scholar
[2]Ahmed, A. and Rhoades, B. E., ‘Some common fixed point theorems for compatible mappings’, Indian J. Pure Appl. Math. 32. (2001), 1247—1254.Google Scholar
[3]Assad, N. A., ‘Fixed point theorems for set valued transformations on compact sets’, Boll. Un. Math. hal. (4) 8 (1973), 1—7.Google Scholar
[4]Assad, N. A. and Kirk, W. A.., ‘Fixed point theorems for set valued mappings of contractive type’, Pacific J. Math. 43 (1972), 553—562.CrossRefGoogle Scholar
[5]Ćirić, Lj. B., ‘Fixed points for generalized multi-valued mappings’, Mat. Vesnik 9 (1972), 265—272.Google Scholar
[6]Ćirić, Lj. B., ‘A remark on rhoades fixed point theorem for non-self mappings’, Internal J.Math. Math. Sci. 16(1993), 397—400.Google Scholar
[7]Ćirić, Lj. B., ‘Quasi-contraction non-self mappings on banach spaces’, Bull. Acad. Serbe Sci. Arts 23 (1998), 25—31.Google Scholar
[8]Ćirić, Lj. B., Ume, M. S., Khan, M. S. and Pathak, H. K., ‘On some non-self mappings’, Math. Nachr. 251 (2003), 28—33.CrossRefGoogle Scholar
[9]Ćirić, Lj. B. and Ume, J. S., ‘Some common fixed point theorems for weakly compatible mappings’, J. Math. Anal. Appl. 314 (2006), 488—499.CrossRefGoogle Scholar
[10]Hadzic, O., ‘A theorem on coincidence points for multi-valued mappings in convex metric spaces’, Zb. Radova Univ. u Novom Sadu 19 (1989), 233—240.Google Scholar
[11]Itoh, S., ‘Multi-valued generalized contractions and fixed point theorems’, Comment. Math. Univ. Carolin. 18 (1977), 247—258.Google Scholar
[12]Jungck, G., ‘Compatible mappings and common fixed points’, Internal J. Math. Math. Sci. 9(1986), 771—779.Google Scholar
[13]Kaneko, H. and Sessa, S., ‘Fixed point theorems for compatible multi-valued and single-valued mappings’, Internal J. Math. Math. Sci. 12 (1989), 257—262.Google Scholar
[14]Khan, M. S., ‘Common fixed point theorems for multi-valued mappings’, Pacific J. Math. 95(1981), 337—347.CrossRefGoogle Scholar
[15]Markin, J. T., ‘A fixed point theorem for set-valued mappings’, Bull. Amer. Math. Soc. 74 (1968), 639—640.CrossRefGoogle Scholar
[16]Nadler, S. B., ‘Multi-valued contraction mappings’, Pacific J. Math. 30 (1969), 475–488CrossRefGoogle Scholar
[17]Ray, B. K., ‘On Ćirić's fixed point theorem’, Fund. Math. 94 (1977), 221—229.CrossRefGoogle Scholar
[18]Rhoades, B. E., ‘A. fixed point theorem for some non-self mappings’, Math. Japon. 23 (1978), 457—459.Google Scholar
[19]Rhoades, B. E., ‘A fixed point theorem for non-self set-valued mappings’, Internat. J.Math. Math. Sci. 20 (1997), 9—12.CrossRefGoogle Scholar
[20]Sastry, K. P. R., Naidu, S. V. R. and Prasad, J. R., ‘Common fixed points for multi-maps in a metric space’, Nonlinear Anal. 13 (1989), 221—229.Google Scholar
[21]Tsachev, T. and Angelov, V. G., ‘Fixed points of non-self mappings and applications’, Nonlinear Anal. 21 (1993), 9—16.CrossRefGoogle Scholar