An iterative method for solving split minimization problem in Banach space with applications
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Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (242)
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JOLAOSO, Lateef Olakunle, OGBUISI, Ferdinard Udochukwu, MEWOMO, Oluwatosin Temitope. An iterative method for solving split minimization problem in Banach space with applications. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2021, nr. 1-2(95-96), pp. 3-30. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1-2(95-96) / 2021 / ISSN 1024-7696 /ISSNe 2587-4322

An iterative method for solving split minimization problem in Banach space with applications

CZU: 517.5+517.9
MSC 2010: 47H06, 47H09, 49J53, 65K10.

Pag. 3-30

Jolaoso Lateef Olakunle1, Ogbuisi Ferdinard Udochukwu12, Mewomo Oluwatosin Temitope1
 
1 University of KwaZulu-Natal,
2 DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)
 
 
Disponibil în IBN: 3 decembrie 2021


Rezumat

The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in p-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.

Cuvinte-cheie
split feasibility problems, split minimization problems, proximal operators, fixed point problems, inverse problems, Bregman distance, soft thresholding, Banach spaces

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