PICARD TYPE ITERATIVE METHOD WITH APPLICATIONS TO MINIMIZATION PROBLEMS AND SPLIT FEASIBILITY PROBLEMS

Erturk M., GÜRSOY F., Ansari Q. H., KARAKAYA V.

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, cilt.21, sa.4, ss.943-951, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 4
  • Basım Tarihi: 2020
  • Dergi Adı: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.943-951
  • Anahtar Kelimeler: Convex minimization problems, fixed point problems, split feasibility problems, gradient projection method, picard type iterative methods, convergence analysis, ALGORITHM
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we study convergence analysis of a Picard type iterative algorithm for finding fixed points of nonexpansive mappings in the setting of Hilbert spaces. As an application of our result, we propose a new gradient projection algorithm for solving convex minimization problems and derive weak convergence result of such algorithm. An example is presented to illustrate our algorithm and result. As another application of our result, we present an algorithm for solving split feasibility problems and discuss the weak convergence of the algorithm.