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Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces. (English) Zbl 1215.65104
Authors’ abstract: We modify Halpern and Mann’s iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.
65J15Equations with nonlinear operators (numerical methods)
46B20Geometry and structure of normed linear spaces
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