Open access

DOI: 10.24193/fpt-ro.2017.1.28

Authors: Yekini Shehu

Abstract: This paper is concerned with an algorithmic solution to the proximal split feasibility problem which is also a fixed point of a k-strictly pseudocontractive mapping in Hilbert spaces. Under some assumptions on the parameters in our iterative algorithm, we first establish a strong convergence theorem for a problem of finding a point which minimizes a proper convex lower-semicontinuous function ƒ which is also a fixed point of a k-strictly pseudocontractive mapping such that its image under a bounded linear operator A minimizes another proper convex lower-semicontinuous function g and secondly prove another strong convergence result for a problem of finding a point which minimizes a proper convex lower-semicontinuous function ƒ which is also a fixed point of a k-strictly pseudocontractive mapping such that its image under a bounded linear operator A minimizes locally lower semicontinuous, prox-bounded and prox-regular function g. In all our results in this work, our iterative schemes are proposed with a way of selecting the step-sizes such that their implementation does not need any prior information about the operator norm because the calculation or at least an estimate of the operator norm ||A|| is very difficult, if it is not an impossible task. Our result complement many recent and important results in this direction.

Key Words and Phrases: proximal split feasibility problems, Moreau-Yosida approximate, prox-regularity, k-strictly pseudocontractive mapping, fixed point, strong convergence, Hilbert spaces.

2010 Mathematics Subject Classification: 49J53, 65K10, 49M37, 47H10, 90C25.

Published on-line: March 1st, 2017.

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