Nadler’s type principle with high order of convergence |
| |
Authors: | Quanita Kiran Tayyab Kamran |
| |
Institution: | Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan |
| |
Abstract: | Recently Proinov P.D. Proinov, A generalization of the Banach contraction principle with high order of convergence of successive approximations, Nonlinear Analysis (2006), doi:10.1016/j.na.2006.09.008] generalized Banach contraction principle with high order of convergence. We extend some results of Proinov to the case of multi-valued maps from a complete metric space X into the space of all nonempty proximinal closed subsets of X. Our results not only generalize Nadler’s fixed-point theorem (in the case when T is a mapping from a complete metric space X into the space of all nonempty proximinal closed subsets of X) but also gives high order of convergence. As an application, we obtain an existence theorem for first-order initial value problem. |
| |
Keywords: | 47H10 54H25 |
本文献已被 ScienceDirect 等数据库收录! |
|