An Ishikawa-type Iterative Algorithm for Solving A Generalized Variational Inclusion Problem Involving Difference of Monotone Operators.

Ishtyak, Mohd; Ahmad, Rais

In this paper, we study a generalized variational inclusion problem involving difference of monotone operators in Hilbert spaces. We established equivalence between the generalized variational inclusion problem and a fixed point problem. We establish an Ishikawa type iterative algorithm for solving a generalized variational inclusion problem involving difference of monotone operators, which is more general than Mann-type iterative algorithm. An existence result as well as a convergence result are proved separately. The problem of this paper is more general than many existing problems in the literature. Several special cases of generalized variational inclusion problem involving difference of monotone operators are also mentioned.

ITERATIVE methods (Mathematics); FIXED point theory; MONOTONE operators; OPERATOR theory; STOCHASTIC convergence

Applications & Applied Mathematics, 2018, Vol 13, Issue 1, p248

1932-9466

Academic Journal