{
  "id": "1611.04136",
  "version": "v1",
  "published": "2016-11-13T13:43:57.000Z",
  "updated": "2016-11-13T13:43:57.000Z",
  "title": "Relation-theoretic metrical fixed point theorems under nonlinear contractions",
  "authors": [
    "Md Ahmadullah",
    "Mohammad Imdad",
    "Rqeeb Gubran"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those contained in Samet and Turinici [Commun. Math. Anal. 13, 82-97 (2012)] and Alam and Imdad [J. Fixed Point Theory Appl. 17(4), 693-702 (2015)]. Interestingly a corollary to one of our main results proved under symmetric closure of any binary relation remains a sharpened version of a theorem due to Samet and Turinici. Finally, we use examples to highlight the realized improvements in the results proved in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-13T13:43:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H10",
      "54H25"
    ],
    "keywords": [
      "relation-theoretic metrical fixed point theorems",
      "nonlinear contractions",
      "arbitrary binary relation",
      "binary relation remains",
      "fixed point theory appl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}