An iterative method for solving split minimization problem in Banach space with applications

Lateef Olakunle Jolaoso, Ferdinard Udochukwu Ogbuisi, Oluwatosin Temitope Mewomo

Research output: Contribution to journalArticlepeer-review


The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in p-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.

Original languageEnglish
Pages (from-to)3-30
Number of pages28
JournalBuletinul Academiei de Stiinte a Republicii Moldova. Matematica
Issue number1-2
Publication statusPublished - 2021
Externally publishedYes


  • Banach spaces
  • Bregman distance
  • fixed point problems
  • inverse problems
  • proximal operators
  • soft thresholding
  • split feasibility problems
  • split minimization problems


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