- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Fixed points of a certain class of mappings in uniformly convex Banach spaces Bull. Korean Math. Soc. 1997 Vol. 34, No. 3, 385-394 Balwant Singh Thakur and Jong Soo Jung , Dong-A University Abstract : In this paper, we prove in p-uniformly convex space a fixed point theorem for a class of mappings $T$ satisfying: for each $x,\ y$ in the domain and for $n = 1,\ 2,\ 3,\ \cdots,$ \aligned \Vert T^n x - T^n y \Vert \le a \cdot \Vert x - y \Vert &+ b(\Vert x - T^nx \Vert + \Vert y - T^ny \Vert)\\ &\qquad + c(\Vert x - T^ny \Vert + \Vert y - T^nx \Vert), \endaligned where $a,\ b,\ c$ are nonnegative constants satisfying certain conditions. Further we establish some fixed point theorems for these mappings in a Hilbert space, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{p,k}$ for $1 < p < \infty$ and $k \ge 0$. As a consequence of our main result, we also extend the results of Goebel and Kirk [7], Lim [8], Lifshitz [12], Xu [20] and others. Keywords : $p$-uniformly convex Banach space, normal structure, asymptotic center, fixed points MSC numbers : 47H10 Downloads: Full-text PDF