Relaxed resolvent operator for solving a variational inclusion problem

  • Iqbal Ahmad Aligarh Muslim University, Aligarh, India
  • Mijanur Rahaman Aligarh Muslim University, Aligarh, India
  • Rais Ahmad Aligarh Muslim University, Aligarh, India
DOI: https://doi.org/10.19139/soic.v4i2.166
Keywords: Relaxed, Inclusion, Space, Algorithm, Lipschitz.

Abstract

In this paper, we introduce a new resolvent operator and we call it relaxed resolvent operator. We prove that relaxed resolvent operator is single-valued and Lipschitz continuous and finally we appropriate the solution of a variational inclusion problem in Hilbert spaces by defining an iterative algorithm based on relaxed resolvent operator. A few concepts like Lipschitz continuity and strong monotonicity are used to prove the main result of this paper. Thus, no strong conditions are used. Some examples are constructed.

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Published
2016-06-01
How to Cite
Ahmad, I., Rahaman, M., & Ahmad, R. (2016). Relaxed resolvent operator for solving a variational inclusion problem. Statistics, Optimization & Information Computing, 4(2), 183-193. https://doi.org/10.19139/soic.v4i2.166
Issue
Vol 4 No 2 (2016)
Section
Research Articles
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