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Weak and strong convergence results for the modified Noor iteration of three quasi-nonexpansive multivalued mappings in Hilbert spaces

Chaolamjiak Watcharaporn (School of Science, University of Phayao, Phayao, Thailand), c-wchp007@hotmail.com
Khan Suhel Ahmad (Department of Mathematics, BITS-Pilani, Dubai Campus, Dubai, UAE), khan.math@gmail.com
Hammad Hasanen A. (Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt), h_elmagd89@yahoo.com
Dutta Hemen (Department of Mathematics, Gauhati University, Guwahati, India), hen_dutta08@rediffmail.com

The paper aims to present an advanced algorithm by taking help of the Noor-iteration scheme along with the inertial technical term for three quasi-nonexpansive multivalued in Hilbert spaces. A weak convergence theorem under certain conditions has been given and added the CQ and shrinking projection methods to our algorithm to obtain certain strong convergence results. Furthermore, numerical experiments are provided by constructing an example and comparison results have also been incorporated.

Keywords: Weak and strong convergence, Quasi-nonexpansive multivalued mapping, Noor-iteration, inertial technical term, CQ and shrinking projection methods