A viscosity projection method for class T mappings

Abstract

In this paper, we firstly introduce a viscosity projection method for the class T mappingswhere Sn = (1 − w)I + wTn, w ∈ (0, 1), Tn ∈ T and prove strong convergence theorems of the proposed method. It is verified that the viscosity projection method converges locally faster than the viscosity method. Furthermore, we present a viscosity projection method for a quasi-nonexpansive and nonexpansive mappings in Hilbert spaces. A numerical test provided in the paper shows that the viscosity projection method converges faster than the viscosity method.

An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications

“…Our results generalize the result of Petruşel and Yao [10] to the case of a sequence of asymptotically nonexpansive mappings and extend the results of Nadezhkina and Takahashi [7], Zeng and Yao [18] and Chen, Zhang and Fan [2]. Other related results are given in [17]- [4].…”

Viscosity approximations considering boundary point method for fixed-point and variational inequalities of quasi-nonexpansive mappings

“…The iteration process of finding fixed point of quasi-nonexpansive mappings have been extensively investigated (see Maingé 2010; Yamada and Ogura 2004;Ghosh and Debnath 1992, 1995, 1997Petryshyn and Williamson 1973;Dotson 1972;Dang and Gao 2013). A classical and frequently used algorithm, the viscosity approximation (Dong and He 2013;Sunthrayuth et al 2016;Katchang and Kuman 2011;Zhou and Wang 2014;Xu 2004;Jung 2010), which is defined as follows:…”