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A new general iterative scheme for split variational inclusion and fixed point problems of \(k\)-strict pseudo-contraction mappings with convergence analysis. (English) Zbl 1382.47018

Summary: In this paper, we modify the general iterative method to approximate a common element of the set of solutions of split variational inclusion problem and the set of common fixed points of a finite family of \(k\)-strictly pseudo-contractive nonself mappings. Strong convergence theorem is established under some suitable conditions in a real Hilbert space, which also solves some variational inequality problems. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors. Finally, some examples to study the rate of convergence and some illustrative numerical examples are presented.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J22 Variational and other types of inclusions
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