## Abstract

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with an (H, η)-monotone operator, its Lips-chitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the establishment of a new equivalence relationship between the graph convergence of a sequence of (H, η)-monotone operators and their associated resolvent operators, respectively, to a given (H, η)-monotone operator and its associated resolvent operator. A new iterative scheme for approximating a common element of the set of solutions of a variational inclusion problem and the set of fixed points of a given total asymptotically nonexpansive mapping is constructed. As an application of the obtained equivalence conclusion concerning graph convergence, under some suitable conditions, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the above-mentioned two sets is proved. Our results improve and generalize the corresponding results of recent works.

Original language | English |
---|---|

Pages (from-to) | 79-100 |

Number of pages | 22 |

Journal | Fixed Point Theory |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - 1 Feb 2023 |

### Bibliographical note

Funding Information:The second author is grateful to King Fahd University of Petroleum and Minerals for providing excellent research facilities.

Publisher Copyright:

© 2023, House of the Book of Science. All rights reserved.

## Keywords

- (H η)-monotone operator
- Total ({a}
- convergence analysis
- fixed point problem
- resolvent method
- variational inclusion problem
- {b}
- φ)-asymptotically nonexpansive mapping

## ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Applied Mathematics