Viscosity implicit iterative algorithms based on generalized contractions for strictly pseudocontractive 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
pseudocontractive mappings. The first scheme is used to approximate a fixed point of a single strictly
pseudocontractive mapping, the second scheme is used to approximate a common fixed point of a finite family of strictly
pseudocontractive mappings, the third scheme is used to approximate a common fixed point of a countable family of strictly
pseudocontractive 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.
Keywords
 Strictly pseudocontraction
 implicit iterative algorithm
 viscosity technique
 generalized contraction
 fixed point.
MSC
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