In this article, the common solutions of various nonlinear problems are investigated based on gradient algorithms. We obtain the strong convergence of the gradient algorithm in the framework of Hilbert spaces. We also give some applications to support the main results.
This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product Morrey-Herz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions.… (More)