A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces

K.O. Aremu ^[1] ; C. Izuchukwu ^[1] ; O.K. Oyewole ^[1] ; O.T. Mewomo ^[1]
1. [1] University of KwaZulu-Natal
  
  University of KwaZulu-Natal
  
  Ethekwini, Sudáfrica
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 305-325
Idioma: inglés
DOI: 10.33044/revuma.1762
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Resumen
- We propose a modified Halpern-type algorithm involving a Lipschitz hemicontractive non-self mapping and the resolvent of a convex function in a Hadamard space. We obtain a strong convergence of the proposed algorithm to a minimizer of a convex function which is also a fixed point of a Lipschitz hemicontractive non-self mapping. Furthermore, we give a numerical example to illustrate and support our method. Our proposed method improves and extends some recent works in the literature.