{
  "id": "2007.02001",
  "version": "v1",
  "published": "2020-07-01T07:50:51.000Z",
  "updated": "2020-07-01T07:50:51.000Z",
  "title": "Fixed point theorems and convergence theorems for a generalized nonexpansive mapping in uniformly convex Banach spaces",
  "authors": [
    "Chang Il Rim",
    "Jong Gyong Kim"
  ],
  "comment": "10 pages, 1 figure, 1 table",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use Sahu([6]) and Thakur([10])'s iterative scheme to establish several convergence theorems in uniformly convex Banach spaces and give an example to show that this scheme converges faster than the scheme in [1]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-01T07:50:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H09",
      "47H10",
      "26A18"
    ],
    "keywords": [
      "uniformly convex banach spaces",
      "fixed point theorems",
      "generalized nonexpansive mapping",
      "convergence theorems",
      "banach space satisfying opials condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}