Convergence theorem for I-asymptotically quasi-nonexpansive mapping in Hilbert space |
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Authors: | Seyit Temir Ozlem Gul |
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Institution: | Department of Mathematics, Arts and Science Faculty, Harran University, 63200 Sanliurfa, Turkey |
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Abstract: | Let H be a Hilbert space with inner product (⋅,⋅) and ‖⋅‖ norm, and let K be weakly compact a subset of H. Let be nonlinear mapping and be a nonlinear bounded mapping. In this paper, we define the I-asymptotically quasi-nonexpansive mapping in Hilbert space. If T is an I-asymptotically quasi-nonexpansive mapping, then we prove that , for u∈K as n→∞, is weakly almost convergent to its asymptotic center. |
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Keywords: | Asymptotic center Asymptotically quasi-nonexpansive mapping Nonlinear ergodic theorems |
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