• East Asian mathematical journal
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• v.27 no.1
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• Design & Manufacturing
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• v.13 no.1
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• pp.5-12
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• 2019

In this paper, we studied the micro tool deflection, micro cutting with low temperature, and deformation of micro ribs caused by cutting forces. First, we performed an integrated machining error compensation method based on captured images of tool deflection shapes in micro cutting process. In micro cutting process, micro tool deflection generates very serious problems in contrast to macro tool deflection. To get the real images of micro tool deflection, it is possible to estimate tool deflection in cutting conditions modeled and to compensate for machining errors using an iterative algorithm correcting tool path. Second, in macro cutting fields, the cryogenic cutting process has been applied to cut the refractory metal but, the serious problem may be generated in micro cutting fields by the cryogenic environment. However, if the proper low temperature is applied to micro cutting area, the cooling effect of cutting heat is expected. Such effect can make the reduction of tool wear and burr formation. For verifying this passibility, the micro cutting experiment at low temperature was performed and SEM images were analyzed. Third, the micro pattern was deformed by the cutting forces and the shape error occurred in the sidewall multi-step cutting process were minimized. As the results, the relationship between the cutting conditions and the deformation of micro-structure during micro cutting process was investigated.