Proximal Point Algorithms for Numerical Reckoning Fixed Points of Hybrid-Type Multivalued Mappings in Hilbert Spaces

Document Type : Original Article

Authors

Kritsada Lerkchaiyaphum ¹

Withun Phuengrattana ²

¹ Department of Mathematics, Faculty of Science and Technology, Nakhon Pathom Rajabhat University, Nakhon Pathom 73000, Thailand.

² Research Center for Pure and Applied Mathematics, Research and Development Institute, Nakhon Pathom Rajabhat University, Nakhon Pathom 73000, Thailand.

10.22034/kjm.2017.46951

Abstract

In this paper, we propose a new iteration process to approximate
minimizers of proper convex and lower semi-continuous functions and
fixed points of $\lambda$-hybrid multivalued mappings in Hilbert
spaces. We also provide an example to illustrate the convergence
behavior of the proposed iteration process and numerically compare
the convergence of the proposed iteration scheme with the existing
schemes.

Keywords

Proximal point algorithm

hybrid multivalued mapping

Ishikawa iteration

S-iteration

Hilbert spaces

Subjects

• 47 Operator theory
• 65 Numerical analysis

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