Indian Journal of Industrial and Applied Mathematics
  • Year: 2013
  • Volume: 4
  • Issue: 2

Application of H(·, ·)-Cocoercive Oper ators for Solving a Set-Valued Variational Inclusion Problem Via a Resolvent Equation Problem

  • Author:
  • R. Ahmad1,, A.H. Siddiqi2,, M. Dilshad3,
  • Total Page Count: 10
  • Published Online: Dec 1, 2013
  • Page Number: 160 to 169

1Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

2S-10, Administrative Block, Gautam Buddha University, Gautam Budh Nagar, Greater Noida, NCR, India

3School of Mathematics and Computer Applications, Thapar University, Patiala-147004, India

*Corresponding Author Email Id: siddiqi.abulhasan@gmail.com

**raisain123@rediffmail.com

***mdilshaad@gmail.com

Abstract

In this paper, we apply H(·, ·)-cocoercive operators due to Ahmad et al.[1] for solving a set-valued variational inclusion problem via a resolvent equation problem. An equivalence of set-valued variational inclusion problem and a fixed point problem is given. We also established a relationship between set-valued variational inclusion problem and a resolvent equation problem. This equivalence is used to suggest an iterative algorithm for solving resolvent equation problem. Some examples are constructed.

Keywords

Variational inclusion, Algorithm, Resolvent equation, Cocoercive operator, 47H19, 49J40