STRONG CONVERGENCE THEOREM SOLUTION BY ITERATION OF NONLINEAR OPERATOR EQUATIONS INVOLVING MONOTONE MAPPINGS

Authors

  • N. N. Araka DEPARTMENT OF MATHEMATICS, FEDERAL UNIVERSITY OF TECHNOLOGY, OWERRI, NIGERIA
  • E. U. Ofoedu DEPARTMENT OF MATHEMATICS, NNAMDI AZIKIWE UNIVERSITY, AWKA, NIGERIA
  • Y. Shehu DEPARTMENT OF MATHEMATICS, UNIVERSITY OF NIGERIA, NSUKKA, NIGERIA
  • H. Zegeye DEPARTMENT OF MATHEMATICS, UNIVERSITY OF GABORONE, BOTSWANA

Abstract

This study focuses on construction of a new explicit iterative scheme for approximation of zeros of nonlinear mappings in reflexive real Banach space with uniformly Gâteaux differentiable norm. In the study, strong convergence of the proposed iterative scheme is proved under mild conditions on the iterative parameters. The scheme does not involve resolvent of the mappings under consideration. Furthermore, applications of results obtained to Dirichlet and Neumann problems are given. Our Theorems improve, extend and unify most of the results that had been proved for this class of mappings.

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Published

2017-01-28

How to Cite

Araka, N. N., Ofoedu, E. U., Shehu, Y., & Zegeye, H. (2017). STRONG CONVERGENCE THEOREM SOLUTION BY ITERATION OF NONLINEAR OPERATOR EQUATIONS INVOLVING MONOTONE MAPPINGS. Journal of the Nigerian Mathematical Society, 35(2), 266–281. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/30

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