A strong convergence theorem for approximation of a zero of the sum of two maximal monotone mappings in Banach spaces

Abstract

The purpose of this paper is to study the method of approximation for a zero of the sum of two maximal monotone mappings in Banach spaces and prove strong convergence of the proposed method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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Funding

Both authors gratefully acknowledge the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST) (ID267269FY17).

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Correspondence to Habtu Zegeye.

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Wega, G.B., Zegeye, H. A strong convergence theorem for approximation of a zero of the sum of two maximal monotone mappings in Banach spaces. J. Fixed Point Theory Appl. 22, 57 (2020). https://doi.org/10.1007/s11784-020-00791-8

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Keywords

  • Firmly nonexpansive
  • Hilbert spaces
  • maximal monotone mapping
  • strong convergence
  • zero points

Mathematics Subject Classification

  • 47H05
  • 47J25
  • 49M27
  • 90C25