## Abstract

The characterizations of m-relaxed monotone and maximal m-relaxed monotone operators are presented and by defining the resolvent operator associated with a maximal m-relaxed monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. By using resolvent operator associated with a maximal m-relaxed monotone operator, an iterative algorithm is constructed for approximating a common element of the set of fixed points of a total uniformly L-Lipschitzian mapping and the set of solutions of a variational inclusion problem involving maximal m-relaxed monotone operators. By employing the concept of graph convergence for maximal m-relaxed monotone operators, a new equivalence relationship between the graph convergence of a sequence of maximal m-relaxed monotone operators and their associated resolvent operators, respectively, to a given maximal m-relaxed monotone operator and its associated resolvent operator is established. At the end, we study the strong convergence of the sequence generated by the proposed iterative algorithm to a common element of the above mentioned sets.

Original language | English |
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Pages (from-to) | 335-348 |

Number of pages | 14 |

Journal | Carpathian Journal of Mathematics |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - 2023 |

### Bibliographical note

Publisher Copyright:© 2023, SINUS Association. All rights reserved.

## Keywords

- Convergence analysis
- Fixed points
- Graph convergence
- Iterative method
- Maximal m-relaxed monotone operators
- Resolvent operators
- Total uniformly L-Lipschitzian mappings
- Variational inclusion problems

## ASJC Scopus subject areas

- Mathematics (all)