On split generalised mixed equilibrium problems and fixed-point problems with no prior knowledge of operator norm

The purpose of this paper is to introduce an iterative algorithm that does not require any knowledge of the operator norm for approximating a solution of a split generalised mixed equilibrium problem which is also a fixed point of a $$\kappa $$κ-strictly pseudocontractive mapping. Furthermore, a strong convergence theorem for approximating a common solution of a split generalised mixed equilibrium problem and a fixed-point problem for $$\kappa $$κ-strictly pseudocontractive mapping was stated and proved in the frame work of Hilbert spaces.

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