Some results on non-expansive mappings and relaxed cocoercive mappings in Hilbert spaces

Xiaolong Qin, Yeol Je Cho, Shin Min Kang
2009 Applicable Analysis  
In this paper, we instigate a viscosity approximation method for nonexpansive and relaxed cocoercive mappings. A strong convergence theorem is established in the framework of Hilbert spaces. 1 2 Y. QING If T 1 = I, the identity mapping, then problem (1.1) is reduced to the following. Find u ∈ C such that (1.2) Variational inequality problem (1.2) was introduced by Stampacchia [1] in 1964. Problem (1.2) has emerged as a fascinating and interesting branch of mathematical and engineering sciences
more » ... gineering sciences with a wide range of applications in industry, finance, economics, social, ecology, regional, pure and applied sciences. In this paper, we use V I(C, T 2 ) to denote the set of solutions of variational inequality problem (1.2). Recently, gradient methods have been extensively investigated for solving problems (1.1) and (1.2); see [2] [3] [4] [5] [6] [7] [8] [9] and the references therein.
doi:10.1080/00036810802308841 fatcat:eiopcnmoqjgfzetakhkkamovf4