Revista de la
Unión Matemática Argentina
Viscosity approximation method for modified split generalized equilibrium and fixed point problems
Hammed Anuoluwapo Abass, Chinedu Izuchukwu, and Oluwatosin Temitope Mewomo
Volume 61, no. 2 (2020), pp. 389–411

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We introduce a viscosity iterative algorithm for approximating a common solution of a modified split generalized equilibrium problem and a fixed point problem for a quasi-pseudocontractive mapping which also solves some variational inequality problems in real Hilbert spaces. The proposed iterative algorithm is constructed in such a way that it does not require the prior knowledge of the operator norm. Furthermore, we prove a strong convergence theorem for approximating the common solution of the aforementioned problems. Finally, we give a numerical example of our main theorem. Our result complements and extends some related works in the literature.