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 - 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 -