an:05612946
Zbl 1203.54042
Klim, D.; Wardowski, D.
Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 11, 5170-5175 (2009).
00254077
2009
j
54H25 54C60 26A18
dynamic process; set-valued nonlinear contraction; fixed point; cone metric space
Summary: Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by \textit{L.-G.\thinspace Huang} and \textit{X.\,Zhang} [J.~Math.\ Anal.\ Appl.\ 332, No.\,2, 1468--1476 (2007; Zbl 1118.54022)] for cone metric spaces and by \textit{D.\,Klim} and \textit{D.\,Wardowski} [J.~Math.\ Anal.\ Appl.\ 334, No.\,1, 132--139 (2007; Zbl 1133.54025)] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above.
Zbl 1118.54022; Zbl 1133.54025