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Convergence Theorems for Pointwise Asymptotically Strict Pseudo-Contractions in Hilbert Spaces |
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| Authors: | Javad Balooee Yeol Je Cho Mehdi Roohi |
| Affiliation: | 1. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iranjavad.balooee@gmail.com;3. Department of Mathematics Education and Research Institute of Natural Sciences, Gyeongsang National University, Chinju, Korea, and Center for General Education, China Medical University, Taichung, Taiwan;4. Department of Mathematics, Faculty of Science, Golestan University, Gorgan, Iran |
| Abstract: | A new class of contractive mappings called pointwise asymptotically ?-strict pseudo-contractions in Hilbert spaces is introduced and weak convergence of the sequence generated by Mann's iterative scheme to a fixed point of a uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mapping T in a Hilbert space is established. Also, a new kind of monotone hybrid method which is a modification of Mann's iterative scheme for finding a common fixed point of an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mappings is proposed. Strong convergence of the sequence generated by the proposedmonotone hybrid method for an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ?-strict pseudo-contractive mappings in a Hilbert space is also shown. The results presented in this article extend and improve some known results in the literature. |
| Keywords: | Common fixed point Mann's iterative method monotone hybrid method pointwise asymptotically ?-strict pseudo-contraction projection operator projection technique weak and strong convergence |