Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces


Authors

Qingqing Cheng - Department of Mathematics and LPMC, Nankai University, Tianjin, 300071, China. Yongfu Su - Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China.


Abstract

In this manuscript, we construct three viscosity implicit iteration schemes based on generalized contractions for strictly pseudo-contractive mappings. The first scheme is used to approximate a fixed point of a single strictly pseudo-contractive mapping, the second scheme is used to approximate a common fixed point of a finite family of strictly pseudo-contractive mappings, the third scheme is used to approximate a common fixed point of a countable family of strictly pseudo-contractive mappings. Furthermore, three strong convergence theorems based on the purposed iterative schemes are established in the framework of Banach spaces. Finally, three numerical examples are also given to show the efficiency and implementation of our schemes. The main results of this paper modify and improve many important recent results in the literature.


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ISRP Style

Qingqing Cheng, Yongfu Su, Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4611--4627

AMA Style

Cheng Qingqing, Su Yongfu, Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces. J. Nonlinear Sci. Appl. (2017); 10(9):4611--4627

Chicago/Turabian Style

Cheng, Qingqing, Su, Yongfu. "Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudo-contractive mappings in Banach spaces." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4611--4627


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