IJPAM: Volume 108, No. 3 (2016)

AN IMPLICIT VISCOSITY TECHNIQUE OF
NONEXPANSIVE MAPPINGS IN HILBERT SPACES

Chahn Yong Jung$^1$, Waqas Nazeer$^2$,
Sayed Fakhar Abbas Naqvi$^3$, Shin Min Kang$^4$
$^{1}$Department of Business Administration
Gyeongsang National University
Jinju 52828, KOREA
$^{2}$Division of Science and Technology
University of Education
Lahore 54000, PAKISTAN
$^{3}$Department of Mathematics
Lahore Leads University
Lahore 54810, PAKISTAN
$^{4}$Department of Mathematics and RINS
Gyeongsang National University
Jinju 52828, KOREA


Abstract. In this paper, we present a new viscosity technique of nonexpansive mappings in Hilbert spaces. The strong convergence theorems of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. We also give applications of the proposed viscosity technique to a more general system of variational inequalities, the constrained convex minimization problem and the $K$-mapping.

Received: April 17, 2016

AMS Subject Classification: 47J25, 47N20, 34G20, 65J15

Key Words and Phrases: viscosity rule, Hilbert space, nonexpansive mapping, variational inequality, minimization problem, $K$-mapping

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DOI: 10.12732/ijpam.v108i3.14 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 3
Pages: 635 -


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