Shrinking projection method for solving inclusion problem and fixed point problem in reflexive Banach spaces. (English) Zbl 07419474
Summary: The purpose of this paper is to find a common element in the intersection of the set of zeros of the inclusion problem of sum of two monotone mappings and the set of fixed points of a Bregman quasi nonexpansive mapping in a reflexive Banach space by using Bregman distance and shrinking projection method. Under suitable conditions, some strong convergence theorems are proved. As applications, we utilize our results to study the convex minimization problem, variational inequality problem.
MSC:
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 49J40 | Variational inequalities |
Keywords:
Bregman distance; Bregman quasi-nonexpansive mapping; Bregman strongly nonexpansive mapping; maximal monotone operator; Bregman inverse strongly monotone mappingReferences:
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