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On general hybrid contractions

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

Published online by Cambridge University Press:  09 April 2009

S. L. Singh  and
S. N. Mishra
S. L. Singh
Affiliation:
Department of Mathematics, Gurukula Kangri University, Hardwar 249404, India
S. N. Mishra
Affiliation:
Department of Mathematics, University of Transkei, Umtata 5100, South Africa, e-mail: [email protected]
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Abstract

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Keywords

hybrid contractionweakly commuting mapscompatible mapsweakly compatible maps

MSC classification

Secondary: 47H10: Fixed-point theorems 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 2 , April 1999 , pp. 244 - 254
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Aubin, J. P. and Ekeland, I., Applied nonlinear analysis (Wiley, New York, 1984).Google Scholar
[2]Baillon, J. B. and Singh, S. L., ‘Nonlinear hybrid contractions on product spaces’, Far East J. Math.Sci. 1(1993), 117–127.Google Scholar
[3]Beg, I. and Azam, A., ‘Fixed points of asymptotically regular multivalued mappings’, J. Austral. Math. Soc. (Series A) 53 (1992), 313–326.CrossRefGoogle Scholar
[4]Corley, H. W., ‘Some hybrid fixed point theorems related to optimization’, J. Math. Anal. Appl. 120 (1980), 528–532.CrossRefGoogle Scholar
[5]Hicks, T. and Rhoades, B. E., ‘Fixed points and continuity for multivalued mappings’, Internat. J. Math. Math. Sci. 15 (1992), 15–30.Google Scholar
[6]Itoh, S. and Takahashi, W., ‘Single-valued mappings, multi-valued mappings and fixed point theorems’, J. Math. Anal. Appl. 59 (1977), 514–521.Google Scholar
[7]Jachymski, J., ‘Common fixed point theorems for some families of maps’, Indian J. Pure Appl. Math. 25 (1994), 925–937.Google Scholar
[8]Jungck, G., ‘Common fixed points for commuting and compatible mappings on compacta’, Proc. Amer. Math. Soc. 103 (1988), 977–983.CrossRefGoogle Scholar
[9]Khan, M. S., Cho, Y. J., Park, W. T. and Mumtaz, T., ‘Coincidence and common fixed points of hybrid contractions‘, J. Austral. Math. Soc. (Series A) 55 (1993), 369–385.Google Scholar
[10]Nadler, S. B. Jr., ’Multivalued contraction mappings’. Pacific J. Math. 30 (1969), 475–188.CrossRefGoogle Scholar
[11]Naimpally, S. A., Singh, S. L. and Whitfield, J. H. M., ‘Coincidence theorems for hybrid contractions’, Math. Nachr. 127 (1986), 177–180.CrossRefGoogle Scholar
[12]Pathak, H. K., ‘Fixed point theorems for weak compatible multi-valued and single-valued mappings’, Acta Math. Hungar. 67 (1995), 69–78.Google Scholar
[13]Rhoades, B. E., Singh, S. L. and Kulshrestha, C., ‘Coincidence theorems for some multi-valued mappings’, Internat. J. Math. Math. Sci. 7 (1984), 429–434.CrossRefGoogle Scholar
[14]Singh, S. L., Ha, K. S. and Cho, Y. J., ‘Coincidence and fixed points of nonlinear hybrid contractions’, Internal. J. Math. Math. Sci. 12 (1989), 247–256.CrossRefGoogle Scholar
[15]Singh, S. L. and Mishra, S. N., ‘Nonlinear hybrid contractions’, J. Natur. Phys. Sci. 5–8 (1991–1994), 191–.Google Scholar
[16]Singh, S. L., ‘Coincidence points, hybrid fixed and stationary points of orbitally weakly dissipative maps’. Math. Japon. 39 (1994), 451–459.Google Scholar
[17]Singh, S. L., ‘Some remarks on coincidences and fixed points’, C. R. Math. Rep. Acad. Sci. Canada 18 (1996), 66–70.Google Scholar
[18]Singh, S. L., Totik, V., ‘On two open problems of contractive mappings’, Publ. Inst. Math. (Beograd) N. S. 34 (1983), 239–242.Google Scholar
[19]Wegrzyk, R., ‘Fixed point theorems for multivalued functions and their applications to functional equations’, Dissertationes Math. (Rozprawy Mat.) 201 (1982), 1–28Google Scholar