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**On variational inclusion and common fixed point problems in \(q\)-uniformly smooth Banach spaces.**
*(English)*
Zbl 1263.47082

Summary: We introduce a general iterative algorithm for finding a common element of the common fixed point set of an infinite family of \(\lambda_i\)-strict pseudocontractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in a \(q\)-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in some references.

### MSC:

47J25 | Iterative procedures involving nonlinear operators |

47J22 | Variational and other types of inclusions |

47H06 | Nonlinear accretive operators, dissipative operators, etc. |

### Keywords:

general iterative algorithm; common fixed point set; infinite family of \(\lambda_i\)-strict pseudocontractions; general system of variational inclusions; inverse strongly accretive operators; \(q\)-uniformly smooth Banach space; strong convergence
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\textit{Y. Song} et al., J. Appl. Math. 2012, Article ID 865810, 20 p. (2012; Zbl 1263.47082)

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### References:

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