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, vol.21, no.4, pp.943-951, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2020
  • Journal Name: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.943-951
  • Keywords: Convex minimization problems, fixed point problems, split feasibility problems, gradient projection method, picard type iterative methods, convergence analysis, ALGORITHM
  • Yıldız Technical University Affiliated: Yes

Abstract

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.