Abstract
The concepts of multiple quasicompatibility for single-valued and multi-valued mappings are defined. Some common fixed- and coincidence-point theorems for single-valued and multi-valued mappings satisfying a ϕ-type condition are obtained by an iteration scheme. The conditions are not assumed to be of a contractive type.
Similar content being viewed by others
References
Y. J. Cho, B. Fisher, and G. S. Genga, “Coincidence theorems for nonlinear hybrid contractions,” Internat. J. Math. Math. Sci. 20(2), 249–256 (1997).
H. Kaneko and S. Sessa, “Fixed-point theorems for compatible multi-valued and single-valued mapping,” Internat. J. Math. Math. Sci. 12(2), 257–262 (1989).
N. Shahzad and T. Kamran, “Coincidence points and R-weakly commuting maps,” Arch. Math. (Brno) 37(3), 179–183 (2001).
H. K. Pathak, “Fixed-point theorems for weak compatible multi-valued and single-valued mapping,” Acta Math. Hungar. 67(1–2), 69–78 (1995).
H. K. Pathak, S. M. Kang, and Y. J. Cho, “Coincidence-and fixed-point theorems for nonlinear hybrid generalized contractions,” Czechoslovak Math. J. 48(2), 341–357 (1998).
S. B. Nadler, “Multivalued contraction mappings,” Pacific J. Math. 30, 475–488 (1969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Matematicheskie Zametki, 2008, Vol. 83, No. 3, pp. 361–369.
The text was submitted by the author in English.
Rights and permissions
About this article
Cite this article
Lai, Y. Common coincidence- and fixed-point theorems for a class of nonlinear hybrid mappings. Math Notes 83, 327–334 (2008). https://doi.org/10.1134/S0001434608030048
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434608030048