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Strong convergence theorems for fixed point problems for strict pseudo-contractions and variational inequalities for inverse-strongly accretive mappings in uniformly smooth Banach spaces

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Abstract

In this paper, we first study a simple viscosity iterative algorithm for finding a fixed point of a nonexpansive mapping in uniformly smooth Banach space and obtain a strong convergence theorem under suitable conditions. Then, we apply our iterative algorithm to find a common element of the set of fixed points for a strict pseudo-contraction and the set of fixed points for a nonexansive mapping in uniformly smooth Banach space. We also apply our main results to find a common element of the set of fixed points for strict pseudo-contraction and nonexpansive mapping, the set of solutions of general variational inequalities for two inverse-strongly accretive mappings and equilibrium problems in uniformly smooth Banach spaces or Hilbert spaces. Finally, two numerical examples are given in support of our main results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Gang Cai

  2. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Yekini Shehu

  3. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Wisconsin, USA

    Olaniyi Samuel Iyiola

Authors
  1. Gang Cai
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  2. Yekini Shehu
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  3. Olaniyi Samuel Iyiola
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Correspondence to Gang Cai.

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This work was supported by the NSF of China (Grant nos. 11401063, 11771063), the Natural Science Foundation of Chongqing (Grant nos. cstc2017jcyjAX0006, cstc2016jcyjA0116), Science and Technology Project of Chongqing Education Committee (Grant nos. KJ1703041, KJZDM201800501, KJ16003162016), the University Young Core Teacher Foundation of Chongqing (Grant nos. 020603011714), Talent Project of Chongqing Normal University (Grant no. 02030307-00024).

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Cai, G., Shehu, Y. & Iyiola, O.S. Strong convergence theorems for fixed point problems for strict pseudo-contractions and variational inequalities for inverse-strongly accretive mappings in uniformly smooth Banach spaces. J. Fixed Point Theory Appl. 21, 41 (2019). https://doi.org/10.1007/s11784-019-0677-z

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  • DOI: https://doi.org/10.1007/s11784-019-0677-z

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