Approximation of fixed points for a new class of generalized non-expansivmappings in Banach spaces

Abdeljawad T., Karaca N., YILDIRIM İ., Mukheimer A.

AIMS Mathematics, cilt.9, sa.5, ss.11958-11974, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024584
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.11958-11974
  • Anahtar Kelimeler: fixed point, generalized non-expansive mappings, uniformly convex Banach spacMathematics
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,µ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.