Convergence Analysis for Generalized Yosida Inclusion Problem with Applications

A new generalized Yosida inclusion problem, involving A-relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence result is quantified in q-uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. Our theoretical assertions are illustrated by a numerical example. In addition, we confirm that the developed method is almost stable for contractions. Further, an equivalent generalized resolvent equation problem is established. Finally, by utilizing the Yosida inclusion problem, we investigate a resolvent equation problem and by employing our proposed method, a Volterra-Fredholm integral equation is examined.

Automated summary

A new generalized Yosida inclusion problem is introduced, which involves an A-relaxed co-accretive mapping. The resolvent and associated generalized Yosida approximation operator are defined, and their characteristics are discussed. The existence result is quantified in q-uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. The theoretical assertions are illustrated with a numerical example. Furthermore, an equivalent generalized resolvent equation problem is established, and a Volterra-Fredholm integral equation is examined using the proposed method.