On split common fixed point and monotone inclusion problems in reflexive Banach spaces. (English) Zbl 07606911
Summary: In this paper, we study split common fixed point problems of Bregman demigeneralized and Bregman quasi-nonexpansive mappings in reflexive Banach spaces. Using the Bregman technique together with a Halpern iterative algorithm, we approximate a solution of split common fixed point problem and sum of two monotone operators in reflexive Banach spaces. We establish a strong convergence result for approximating the solution of the aforementioned problems. It is worth mentioning that the iterative algorithm employ in this article is design in such a way that it does not require prior knowledge of operator norm and we do not employ Fejér monotinicity condition in the strategy of proving our convergence theorem. We apply our result to solve variational inequality and convex minimization problems. The result discuss in this paper extends and complements many related results in literature.
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 |
| 47H10 | Fixed-point theorems |
Keywords:
Bregman quasi-nonexpansive; Bregman demigeneralized mapping; monoton operators; fixed point; iterative scheme; split common fixed point problemReferences:
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