The Institute for Economic and Business Research Faculty of Economics, Shiga University
Abstract
We introduce an iterative scheme generating method (ISGM) for contraction type mappings in Banach spaces. This marks the first time ISGM has been demonstrated in a Banach space setting. Our main theorem can apply to contraction mappings, Kannan mappings, etc., enabling to generate infinitely many iterative schemes for finding fixed points. Several corollaries are presented to show a wide variety of iterative methods which can be generated from the main theorems. We also introduce an application to a variational inequality problem (VIP), highlighting how the various iterative schemes covered in this work are directly useful in optimization techniques.technical repor
