New results on the asymptotic behavior of solutions to a class of second order nonhomogeneous difference equations

✍ Scribed by Behzad Djafari Rouhani; Hadi Khatibzadeh

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 230 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2011.05.062

✦ Synopsis

We investigate the asymptotic behavior of solutions to the following system of second order nonhomogeneous difference equation:

where A is a maximal monotone operator in a real Hilbert space H, {c n } and {θ n } are positive real sequences and {f n } is a sequence in H. We show the weak and strong convergence of solutions and their weighted averages to an element of A -1 (0), which is the asymptotic center of the sequence {u n }, under appropriate assumptions on the sequences {c n }, {θ n } and {f n }. Our results continue our previous work in Djafari Rouhani and Khatibzadeh (2008, 2010) [30,31], by presenting some new results on the asymptotic behavior of solutions, including in particular a completely new strong convergence result, and extend some previous results by Apreutesei (2003) [27,28], Morosanu (1979) [21] and Mitidieri and Morosanu (1985-86) [22] to the nonhomogeneous case and without assuming A to have a nonempty zero set.