A viscosity iterative technique for split variational inclusion and fixed point problems between a Hilbert space and a Banach space |
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Authors: | Chinedu Izuchukwu Chibueze Christian Okeke Felicia Obiageli Isiogugu |
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Institution: | 1.School of Mathematics, Statistics and Computer Science,University of Kwazulu-Natal,Durban,South Africa;2.DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), University of WitWatersrand,Johannesburg,South Africa;3.Department of Mathematics,University of Nigeria,Nsukka,Nigeria |
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Abstract: | The main purpose of this paper is to introduce a viscosity-type iterative algorithm for approximating a common solution of a split variational inclusion problem and a fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common solution of a split variational inclusion problem and a fixed point problem for a multivalued quasi-nonexpansive mapping between a Hilbert space and a Banach space. Furthermore, we applied our results to study a split convex minimization problem. Also, a numerical example of our result is given. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13, 759–775, 2012), Moudafi (J. Optim. Theory Appl. 150, 275–283, 2011), Takahashi and Yao (Fixed Point Theory Appl. 2015, 87, 2015), and a host of other important results in this direction. |
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