Indian Journal of Industrial and Applied Mathematics
  • Year: 2019
  • Volume: 10
  • Issue: 2

Generalized Symmetric Monotone Mapping and its Application for Solving a Set-Valued Variational Inclusion Problem

1Assistant Professor, Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

2Professor, School of Basic Sciences and Research, Sharda University, Greater Noida-201306, India, siddiqi.abulhasan@gmail.com

3Assistant Professor, Department of Mathematical Sciences, Baba Ghulam Shah Badshah University, Rajouri, Jammu and Kashmir, India, javid2iqbal@gmail.com

4Professor, Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India, raisain_123@rediffmail.com

*Corresponding author E-mail: ishtyakalig@gmail.com

MSC: 47J20, 90C33, 47H19.

Abstract

The aim of this paper is to define a generalized symmetric monotone mapping, which involves an identity mapping and a symmetric monotone mapping. The resolvent operator associated with the generalized symmetric monotone mapping is defined and it is shown that it is singlevalued as well as Lipschitz continuous. Finally, a set-valued variational inclusion problem is solved as an application. An example is constructed in support of generalized symmetric monotone mapping and also a Matlab programme showing that M(f, g) is symmetric monotone with respect to f and g is given.

Keywords

Symmetric monotone, Variational inclusion, Lipschitz, Set-valued, Algorithm