System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces

  • Nabin Kumar Sahu Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, India
  • N. K. Mahato PDPM IIITDM, Jabalpur, India
  • R. N. Mohapatra University of Central Florida, Orlando, FL. 32816, USA
DOI: https://doi.org/10.19139/soic.v5i3.238
Keywords: Variational inclusion, Generalized resolvent operator, $2$-uniformly smooth Banach space, Semi-inner product space

Abstract

This paper deals with a new system of nonlinear variational inclusion problems involving $(A,\eta)$-maximal relaxed monotone and relative $(A,\eta)$-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also proved for other system of variational inclusion problems involving relative $(A,\eta)$-maximal monotone mappings and $(H,\eta)$-maximal monotone mappings.

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Published
2017-08-29
How to Cite
Sahu, N. K., Mahato, N. K., & Mohapatra, R. N. (2017). System of nonlinear variational inclusion problems with $(A,\eta)$-maximal monotonicity in Banach spaces. Statistics, Optimization & Information Computing, 5(3), 244-261. https://doi.org/10.19139/soic.v5i3.238
Issue
Vol 5 No 3 (2017)
Section
Research Articles
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