A New Iterative Method for Solving Constrained Minimization, Variational Inequality and Split Feasibility Problems in the Framework of Banach Spaces
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Akutsah, Francis
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Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South AfricaUniv KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa
Akutsah, Francis
[1
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Mebawondu, Akindele Adebayo
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DST NRF Ctr Excellence Math & Stat Sci CoE MaSS, Johannesburg, South Africa
Mt Top Univ, Dept Comp Sci & Math, Prayer City, Ogun State, NigeriaUniv KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa
Mebawondu, Akindele Adebayo
[2
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Pillay, Paranjothi
[1
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Narain, Ojen Kumar
[1
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Igiri, Chinwe Peace
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Mt Top Univ, Dept Comp Sci & Math, Prayer City, Ogun State, NigeriaUniv KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa
Igiri, Chinwe Peace
[3
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机构:
[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa
[2] DST NRF Ctr Excellence Math & Stat Sci CoE MaSS, Johannesburg, South Africa
[3] Mt Top Univ, Dept Comp Sci & Math, Prayer City, Ogun State, Nigeria
In this paper, we introduce a new type of modified generalized alpha-nonexpansive mapping and establish some fixed point properties and demiclosedness principle for this class of mappings in the framework of uniformly convex Banach spaces. We further propose a new iterative method for approximating a common fixed point of two modified generalized alpha-nonexpansive mappings and present some weak and strong convergence theorems for these map-pings in uniformly convex Banach spaces. In addition, we apply our result to solve a convex-constrained minimization problem, vari-ational inequality and split feasibility problem and present some numerical experiments in infinite dimensional spaces to establish the applicability and efficiency of our proposed algorithm. The ob-tained results in this paper improve and extend some related results in the literature.