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

Altun I., Turkoglu D.

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, cilt.9, sa.1, ss.9-14, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 2007
  • Dergi Adı: JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9-14
  • Anahtar Kelimeler: fixed points, contractive condition of operator type
  • Gazi Üniversitesi Adresli: Hayır

Özet

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.