Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T17:41:40.511Z Has data issue: false hasContentIssue false
  • English
  • Français

On general hybrid contractions

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

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]
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

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