Some Fixed Point Theorems in Extended b-metric Spaces

ÖZTÜRK V., TÜRKOĞLU A. D., Ansari A. H.

5th International Conference of Mathematical Sciences, ICMS 2021, İstanbul, Türkiye, 23 - 27 Haziran 2021, cilt.2483 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 2483
  • Doi Numarası: 10.1063/5.0118603
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: almost contraction, extended b-metric, fixed point
  • Gazi Üniversitesi Adresli: Evet

Özet

© 2022 American Institute of Physics Inc.. All rights reserved.Banach contraction principle is one of the earlier and main results in fixed point theory. Banach contraction principle which guarantees existence and uniqueness of fixed point was proved in complete metric spaces in 1922 by Banach. According to this principle, ”let (X, d) be a complete metric space and f : X → X be a mapping. If there exists a constant 0 ≤ k < 1 such that for all x, y ∈ X, d(f x, f y) ≤ k.d(x, y), then f has a unique fixed point”. In this work, we define almost contraction in extended b-metric space and prove some fixed point theorems for mappings satisfying this type contraction.