Generalized Viscosity Three-step Implicit Double Midpoint Rule for Non-expansive Mappings
The iterative algorithm for fixed points is a hot topic in nonlinear functional analysis research.The viscosity algorithm for constructing a new generalized three-step implicit double midpoint rule for non-expanding mappings with fixed points in a uniformly smooth Banach spaces is proposed.Under appropriate conditions,the dual mapping definition and Banach limit definition and techniques are used to prove that the iterative sequence generated by this algorithm strongly converges to the common element of the common fixed point set of three non-expanding mappings,and the inference in special cases is given.The results improve and generalize the relevant results in recent literature.
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