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Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces |
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| Authors: | Weerayuth Nilsrakoo Satit Saejung |
| Institution: | a Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand b Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand c The Centre of Excellence in Mathematics, CHE, Sriayudthaya Rd, Bangkok 10400, Thailand |
| Abstract: | In this paper, 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. |
| Keywords: | Relatively quasi-nonexpansive mapping Relatively nonexpansive mapping Nonspreading mapping Generalized nonexpansive mapping Generalized nonexpansive type mapping Maximal monotone operator |
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