A Hybrid Method for Monotone Variational Inequalities Involving Pseudocontractions

• Main Authors: Marino Giuseppe, Liou Yeong-Cheng, Yao Yonghong
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/180534

<p/> <p>We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point <inline-formula> <graphic file="1687-1812-2011-180534-i1.gif"/></inline-formula> with the property <inline-formula> <graphic file="1687-1812-2011-180534-i2.gif"/></inline-formula> such that <inline-formula> <graphic file="1687-1812-2011-180534-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2011-180534-i4.gif"/></inline-formula> where <inline-formula> <graphic file="1687-1812-2011-180534-i5.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2011-180534-i6.gif"/></inline-formula> are two pseudocontractive self-mappings of a closed convex subset <inline-formula> <graphic file="1687-1812-2011-180534-i7.gif"/></inline-formula> of a Hilbert space with the set of fixed points <inline-formula> <graphic file="1687-1812-2011-180534-i8.gif"/></inline-formula>. Assume the solution set <inline-formula> <graphic file="1687-1812-2011-180534-i9.gif"/></inline-formula> of (VI) is nonempty. In this paper, we introduce one implicit scheme which can be used to find an element <inline-formula> <graphic file="1687-1812-2011-180534-i10.gif"/></inline-formula>. Our results improve and extend a recent result of (Lu et al. 2009).</p>