More general viscosity implicit midpoint rule for nonexpansive mapping with applications

Volume 10, Issue 5, pp 2743--2756 http://dx.doi.org/10.22436/jnsa.010.05.41

Publication Date: May 25, 2017 Submission Date: March 12, 2017

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Authors

Hui-Ying Hu - Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.

Abstract

The more general viscosity implicit midpoint rule of fixed point of nonexpansive mapping in Hilbert space is established. The strong convergence of this rule is proved under certain assumptions imposed on the sequence of parameters, which, in addition, is the unique solution of the variational inequality problem. Applications to variational inequalities, hierarchical minimization problems, Fredholm integral equations, and nonlinear evolution equations are included. The results presented in this work may be treated as an improvement, extension and refinement of some corresponding ones in the literature.

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Keywords

• More general viscosity implicit midpoint rule
• nonexpansive mapping
• fixed point problem
• iterative scheme
• variational inequality.

MSC

•  47J25
•  47N20
•  34G20
•  65J15

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