\(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces


Authors

Rais Ahmad - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India. Mohammad Dilshad - Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.


Abstract

In this paper, we define \(H(.,.)-\eta\)-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent operator. We prove the Lipschitz continuity of the resolvent operator associated with \(H(.,.)-\eta\)-cocoercive operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved. Some examples are given.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

Rais Ahmad, Mohammad Dilshad, \(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 5, 334--344

AMA Style

Ahmad Rais, Dilshad Mohammad, \(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces. J. Nonlinear Sci. Appl. (2012); 5(5):334--344

Chicago/Turabian Style

Ahmad, Rais, Dilshad, Mohammad. "\(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces." Journal of Nonlinear Sciences and Applications, 5, no. 5 (2012): 334--344


Keywords


MSC


References