an:05989176
Zbl 1228.54041
Kadelburg, Zoran; RadenoviÄ‡, Stojan
Some results on set-valued contractions in abstract metric spaces
EN
Comput. Math. Appl. 62, No. 1, 342-350 (2011).
0898-1221
2011
j
54H25 54C60 47H04 47H09 47H10 65J15
normal and nonnormal cones; cone metric space; fixed point; set-valued contraction; endpoint
Summary: In this paper, the concept of contractive set-valued maps in the frame of abstract metric spaces is studied and the existence of fixed points for such maps is guaranteed under certain conditions. Consequently, several known fixed point results are either generalized or extended, including the corresponding recent fixed point results of \textit{D. Wardowski} [Nonlinear Anal., Theory Methods Appl. 71, No. 1-2, A, 512--516 (2009; Zbl 1169.54023)] as well as \textit{D. Klim} and \textit{D. Wardowski} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, A, 5170--5175 (2009; Zbl 1203.54042)]. Examples are given to show that our results are distinct from the existing ones.
1169.54023; 1203.54042