TY - JOUR

T1 - Strong convergence theorem for approximating zero of accretive operators and application to Hammerstein equation

AU - Oyewole, Olawale Kazeem

AU - Aibinu, Matthew Olajiire

AU - Jolaoso, Lateef Olakunle

AU - Mewomo, Oluwatosin Temitope

N1 - Funding Information:
The second author acknowledges with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF CoE-MaSS) Doctoral Bursary. Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the CoE-MaSS.
Publisher Copyright:
© 2023,Nonlinear Studies.All Rights Reserved.

PY - 2023

Y1 - 2023

N2 - Let C be a nonempty, closed and convex subset of a real q-uniformly smooth Banach space X which admits a weakly sequentially continuous generalized duality mapping jq. We study the approximation of the zero of a strongly accretive operator A: X →X which is also the fixed point of a k strictly pseudo-contractive self mapping on C. We introduce a new algorithm and prove its strong convergence to the zero of A and fixed point of T. The obtained result is applied to the solution of nonlinear integral equation of the Hammerstein type. Our result extends some existing results in literature.

AB - Let C be a nonempty, closed and convex subset of a real q-uniformly smooth Banach space X which admits a weakly sequentially continuous generalized duality mapping jq. We study the approximation of the zero of a strongly accretive operator A: X →X which is also the fixed point of a k strictly pseudo-contractive self mapping on C. We introduce a new algorithm and prove its strong convergence to the zero of A and fixed point of T. The obtained result is applied to the solution of nonlinear integral equation of the Hammerstein type. Our result extends some existing results in literature.

UR - http://www.scopus.com/inward/record.url?scp=85150239458&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85150239458

SN - 1359-8678

VL - 30

SP - 23

EP - 41

JO - Nonlinear Studies

JF - Nonlinear Studies

IS - 1

ER -