Korean J. Math. Vol. 24 No. 2 (2016) pp.199-213
DOI: https://doi.org/10.11568/kjm.2016.24.2.199

A resolvent approach for solving a set-valued variational inclusion problem using weak-RRD set-valued mapping

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Published: Mar 30, 2016
Keywords:
Algorithm, Inclusion, Mapping, Resolvent, Space.
Mathematics Subject Classification:
49J40, 47H05.

Main Article Content

Iqbal Ahmad
Department of Mathematics Aligarh Muslim University Aligarh 202002, India
Rais Ahmad
Department of Mathematics Aligarh Muslim University Aligarh 202002, India
Javid Iqbal
Department of Mathematical Sciences Baba Ghulam Shah Badshah University Rajouri, Jammu and Kashmir, India

Abstract

The resolvent operator approach of [1] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.


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