Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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CONVERGENCE ANALYSIS OF VISCOSITY IMPLICIT RULES OF NONEXPANSIVE MAPPINGS IN BANACH SPACES

  • Mathew O. Aibinu (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal, Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)) ;
  • Jong Kyu Kim (Department of Mathematics Education, Kyungnam University)
  • Published : 20191200

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Abstract

In this paper, the study of implicit viscosity approximation methods for non-expansive mappings in Banach spaces is explored. A new iterative sequence is introduced for the class of nonexpansive mappings in Banach spaces. Suitable conditions are imposed on the control parameters to prove a strong convergence theorem. Moreover, the strong convergence of the newly introduced sequence to a fixed point of a nonexpansive mapping is obtained which also solves the variational inequality problem. These results are improvement and extension of some recent corresponding results announced.

Keywords