Strong convergence theorem for solving split equality fixed point problem which does not involve the prior knowledge of operator norms

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

2 School of Mathematics‎, ‎Statistics and Computer Science‎, ‎University of KwaZulu-Natal‎, ‎Durban‎, ‎South Africa.

3 Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Wisconsin, USA

Abstract

‎Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space‎. ‎So many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎but as widely known the computation of these algorithms may be difficult and for this reason‎, ‎some researchers have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm‎. ‎To the best of our knowledge most of the works in literature that do not involve the calculation or estimation of the operator norm only obtained weak convergence results‎. ‎In this paper, by appropriately modifying the simultaneous iterative algorithm introduced by Zhao‎, ‎we state and prove a strong convergence result for solving split equality problem‎. ‎We present some applications of our result and then give some numerical example to study its efficiency and implementation at the end of the paper‎.

Keywords

Main Subjects

References

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Bulletin of the Iranian Mathematical Society
Volume 43, Issue 2
April 2017
Pages 349-371

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History

  • Receive Date: 16 July 2014
  • Revise Date: 23 November 2015
  • Accept Date: 24 November 2015

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