Total asymptotically nonexpansive mappings and generalized variational-like inclusion problems in semi-inner product spaces

This paper focuses on investigating the problem of finding a common element of the set of solutions of a generalized nonlinear implicit variational-like inclusion problem involving an (A, eta)-maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. and the set of fixed points of a total asymptotically nonexpansive mapping. To achieve such a purpose, a new iterative algorithm is constructed. Applying the concepts of graph convergence and generalized resolvent operator associated with an (A, eta)-maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a point belonging to the intersection of the two sets mentioned above is proved.

Automated summary

This paper investigates a generalized nonlinear implicit variational-like inclusion problem involving an (A, eta)-maximal m-relaxed monotone mapping and the set of fixed points of a total asymptotically nonexpansive mapping. A new iterative algorithm is constructed and the strong convergence of the sequence generated by the algorithm is proven to a point belonging to the intersection of the two sets.