Best proximity point results of iterated function systems for α-ψ-contractions

Aslantas M., Bachay A. H., Sahin H., TÜRKOĞLU A. D.

AIMS Mathematics, cilt.10, sa.8, ss.19106-19125, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 8
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3934/math.2025854
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.19106-19125
  • Anahtar Kelimeler: best proximity point, fractals, iterated function systems
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we present two new concepts, called α-ψ-iterated function system and α-ψ-proximal iterated function system, by using α-ψ-contractions and α-ψ-proximal contractions. Hence, we extended and generalized some definitions existing in the literature. We present some results that determine the necessary conditions to obtain a fractal with an attractor in the mentioned systems. Finally, some interesting examples are presented to apply our results.