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The split common fixed point problem for multivalued demicontractive mappings and its applications. (English) Zbl 07086841
Summary: In this article, we consider the split common fixed point problem for two infinite families of multivalued mappings in real Hilbert spaces. We introduce an algorithm based on the viscosity method for solving the split common fixed point problem for two infinite families of multivalued demicontractive mappings. We establish a strong convergence result under some suitable conditions. As applications, we also apply our main result to the split variational inequality problem and the split common null point problem. Finally, we give the numerical example for supporting our main theorem.

##### MSC:
 47H10 Fixed-point theorems 47J25 Iterative procedures involving nonlinear operators 54H25 Fixed-point and coincidence theorems (topological aspects)
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