Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2018; 33(3): 767-786

Online first article July 11, 2018      Printed July 31, 2018

https://doi.org/10.4134/CKMS.c170074

Copyright © The Korean Mathematical Society.

Weak and strong convergence theorems for the modified Ishikawa iteration for two hybrid multivalued mappings in Hilbert spaces

Watcharaporn Cholamjiak, Natchaphan Chutibutr, Siwanat Weerakham

University of Phayao, University of Phayao, University of Phayao

Abstract

In this paper, we introduce new iterative schemes by using the modified Ishikawa iteration for two hybrid multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. We use CQ and shrinking projection methods with Ishikawa iteration for obtaining strong convergence theorems. Furthermore, we give examples and numerical results for supporting our main results.

Keywords: weak convergence, strong convergence, common fixed point, hybrid multivalued mapping, Ishikawa iteration

MSC numbers: 47H10, 54H25