Weak and strong convergence theorems of an implicit iteration for a countable family of continuous pseudocontractive mappings |
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| Authors: | Daruni Boonchari Satit Saejung |
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| Institution: | aDepartment of Mathematics, Mahasarakham University, Maha Sarakham 44150, Thailand;bDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand |
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| Abstract: | To approximate a common fixed point of a countable family of continuous pseudocontractive mappings, we introduce an implicit iteration sequence. A necessary and sufficient condition for the convergence of a sequence of such iterates for countably many continuous pseudocontractive mappings is given. We also prove the convergence theorems of an implicit iteration sequence for a countable family of strictly pseudocontractive mappings. |
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| Keywords: | Convergence theorem Implicit iteration Continuous pseudocontractive mapping Strictly pseudocontractive mapping |
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