## Abstract

A new generalized Yosida inclusion problem, involving (Formula presented.) -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.

Original language | English |
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Article number | 1409 |

Journal | Mathematics |

Volume | 11 |

Issue number | 6 |

DOIs | |

State | Published - Mar 2023 |

### Bibliographical note

Funding Information:This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444).

Publisher Copyright:

© 2023 by the authors.

## Keywords

- Volterra–Fredholm integral equation
- Yosida inclusion
- almost stability
- iterative algorithm
- resolvent equation

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Mathematics (all)
- Engineering (miscellaneous)