On characterizations of fixed and common fixed points
The authors introduce the concept of \(L\)-mapping which is equivalent to the concept of \(C\)-mapping introduced by \textit{S. Zhang} [Proc. Am. Math. Soc. 97, 343-346 (1986; Zbl 0593.54045)] and establish criteria for the existence of fixed points of \(L\)-mappings. By using the ideas of Jungck and Dien, the authors also obtain some necessary and sufficient conditions for the existence of fixed and common fixed points of continuous mappings. The results presented in this paper generalize, improve and unify the corresponding results of \textit{S. Zhang} [loc. cit.], \textit{Nguyen Huu Dien} [J. Math. Anal. Appl. 187, No. 1, 76-90 (1994; Zbl 0810.54034)], \textit{B. Fisher} [Math. Semin. Notes, Kobe Univ. 7, 81-84 (1979; Zbl 0415.54030)] and \textit{G. Jungck} [Am. Math. Mon. 83, 261-263 (1976; Zbl 0321.54025)].
scientific article; zbMATH DE number 1218615
scientific article