A fixed point theorem for mappings satisfying a general contractive condition of operator type


Altun I., Turkoglu D.

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, vol.9, no.1, pp.9-14, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2007
  • Title of Journal : JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.9-14
  • Keywords: fixed points, contractive condition of operator type

Abstract

In this paper, we prove a fixed point theorem for mappings satisfying a general contractive condition of operator type. In short, we are going to study mappings T : X -> X for which there exists a real number lambda is an element of (0, 1) such that for each x, y is an element of X one has O(f; d(Tx, Ty)) <= lambda O(f; m(x, y)), where O(f;center dot) and f are defined in first section. Also in first section, we give some examples for O(f;center dot). The second section contains the main result. In last section, we give some remarks and an example. This example shows that the mapping T is not satisfying ciric's generalized contraction but it is satisfying a generalized operator type contraction.