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1. The generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces.

Author

Shin Min Kang, Ul Haq, Absar, Nazeer, Waqas, and Ahmad, Iftikhar

Subjects
*MATHEMATICAL mappings, *STOCHASTIC convergence, *MATHEMATICS, *NONEXPANSIVE mappings, *NONLINEAR operators
Abstract

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

Published
2019

2. A new extragradient method for the split feasibility and fixed point problems.

Author

Ming Zhao and Yunfei Du

Subjects
*FIXED point theory, *NONEXPANSIVE mappings, *MATHEMATICAL mappings, *NONLINEAR operators, *MATHEMATICS
Abstract

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

Published
2019