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Paper's Title:

Algorithms for Nonlinear Problems Involving Strictly Pseudocontractive Mappings

Author(s):

Mathew Olajiire Aibinu1, Surendra Colin Thakur2, Sibusiso Moyo3

1Institute for Systems Science & KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.

1DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: 
moaibinu@yahoo.com mathewa@dut.ac.za

2 KZN E-Skill CoLab,
Durban University of Technology,
Durban 4000,
South Africa.
E-mail: 
thakur@dut.ac.za

3Institute for Systems Science & Office of the DVC Research, Innovation & Engagement Milena Court,
Durban University of Technology,
 Durban 4000,
South Africa.
E-mail:
dvcrie@dut.ac.za

 

Abstract:

The puzzles in approximating a fixed point of nonlinear problems involving the class of strictly pseudocontractive mappings are conquered in this paper through viscosity implicit rules. Using generalized contraction mappings, a new viscosity iterative algorithm which is implicit in nature is proposed and analysed in Banach spaces for the class of strictly pseudocontractive mappings. The computations and analysis which are used in the proposed scheme are easy to follow and this gives rooms for a broad application of the scheme. It is obtained that the proposed iterative algorithm converges strongly to a fixed point of a μ-strictly pseudocontractive mapping which also solves a variational inequality problem. The result is also shown to hold for finite family of strictly pseudocontractive mappings. A numerical example is given to show the skillfulness of the proposed scheme and its implementation.


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