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**Outer approximation method for zeros of sum of monotone operators and fixed point problems in Banach spaces.**
*(English)*
Zbl 07457420

Summary: In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

### MSC:

47H06 | Nonlinear accretive operators, dissipative operators, etc. |

47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |

47J05 | Equations involving nonlinear operators (general) |

47J25 | Iterative procedures involving nonlinear operators |

### Keywords:

maximal monotone operators; relatively quasi-nonexpansive mapping; hybrid iterative scheme; split feasibility problem; fixed point problem
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\textit{H. A. Abass} et al., Nonlinear Funct. Anal. Appl. 26, No. 3, 451--474 (2021; Zbl 07457420)

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### References:

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