MODIFIED PROXIMAL POINT ALGORITHM FOR MINIMIZATION AND FIXED POINT PROBLEM IN CAT(0) SPACES

Godwin Chidi Ugwunnadi     (Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Eswatini; Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa, Swaziland)

Abstract


In this paper, we study modified-type proximal point algorithm for approximating a common solution of a lower semi-continuous mapping and fixed point of total asymptotically nonexpansive mapping in complete CAT(0) spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved.


Keywords


Proximal point algorithm, Total asymptotically nonexpansive mapping, Fixed point, $\triangle$ convergence, Strong convergence, CAT(0) space

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References


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DOI: http://dx.doi.org/10.15826/umj.2021.1.010

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