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A proximal point algorithm with perturbation for finding minimizers and fixed points of total asymptotically non-expansive mappings in Hadamard spaces
  • Duangkamon Kitkuan,
  • Naknimit Akkasriworn,
  • Anantachai Padcharoen
Duangkamon Kitkuan
Rambhai Barni Rajabhat University
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Naknimit Akkasriworn
Rambhai Barni Rajabhat University
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Anantachai Padcharoen
Rambhai Barni Rajabhat University

Corresponding Author:[email protected]

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Abstract

In this paper, we are interested in solving the minimization problem and common fixed point problem of a finite family consisting of total asymptotically non-expansive mappings in Hadamard spaces. For finding common solutions to their problems, we introduce a new modified proximal point algorithm with perturbation involving the convex combination technique. Under suitable conditions, Δ-convergence and strong convergence theorems are proved. Finally, we give some examples of numerical.