A new algorithm for solving split common fixed point problem with applications

Author
Mohammad Eslamian
University of Science and Technology of Mazandaran
Abstract
The split common fixed point problem in Banach spaces, is to find a point which belongs to the set of common fixed points of a family of nonlinear mappings in a Banach space such that its image under a linear transformation belongs to the set of common fixed point of another family of nonlinear mappings in a Banach space in the image space. The split common fixed point problem have received much attention due to its applications in many areas of mathematics and engineering sciences such as optimization, image reconstruction, intensity-modulated radiation therapy and image processing. In this paper we present a new algorithm for solving the split common fixed point problem for a finite family of generalized demimetric mappings in uniformly convex and smooth Banach spaces.We establish strong convergence of the sequence generated by the algorithm to a solution of split common fixed point problem which also solves some variational inequality problems. Finally we present some applications of our main result for solving the multiple-set split feasibility problem and the split null point problem.
Keywords
Split common fixed point problem
demimetric mappings
null point problem
Variational inequality problem
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