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

Cheng, Qingqing ¹ ; Su, Yongfu ²

¹ Department of Mathematics and LPMC, Nankai University, Tianjin, 300071, China
² Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 9, p. 4611-4627.

Résumé

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.

Détail

DOI : 10.22436/jnsa.010.09.05

Classification : 47H05, 47H09, 47H10
Keywords: Strictly pseudo-contraction, implicit iterative algorithm, viscosity technique, generalized contraction, fixed point.

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