Convergence point of G-nonexpansive mappings in Banach spaces endowed with graphs applicable in image deblurring and signal recovering problems

Iteration Scheme for Approximating Fixed Points of G-Nonexpansive Maps on Banach Spaces via a Digraph

“…Many mathematicians have been interested in simulated results for image deblurring and signal recovering problems in recent years, also see e.g. [28][29][30]. The reader on the other hand can apply our proposed method to solve image deblurring and signal recovering problems.…”

A novel Noor iterative method of operators with property (E) as concerns convex programming applicable in signal recovery and polynomiography

“…where 𝜁 > 0. As a result, various techniques and iterative schemes have been developed over the years to solve the LASSO problem, see the literature [44][45][46][47]. In this case, we set…”

“…It is well known that the problem () can be solved by the LASSO problem: $$$$ \underset{x\in {\mathrm{\mathbb{R}}}^N}{\min}\frac{1}{2}{\left\Vert y- Ax\right\Vert}_2^2+\zeta {\left\Vert x\right\Vert}_1, $$$$ where $$$ \zeta >0 $$$. As a result, various techniques and iterative schemes have been developed over the years to solve the LASSO problem, see the literature [44–47]. In this case, we set $$$$ T{x}_n= pro{x}_{\zeta g}\left({x}_n-\zeta \nabla f\left({x}_n\right)\right), $$$$ where $$$ f(x)=\frac{1}{2}{\left\Vert y- Ax\right\Vert}_2^2,g(x)=\zeta {\left\Vert x\right\Vert}_1 $$$ and $$$ \zeta \in \left(0,\frac{2}{{\left\Vert A\right\Vert}_2^2}\right) $$$.…”

Modified shrinking projection methods in CAT(0) space

“…Recently, Tripak [17], Suparatulatorn et al [13] and Thianwan and Yambangwai [15] proved the convergence analysis of sequences generated by different iteration processes involving G -nonexpansive mappings in Banach space with directed graph. For more details on modified iteration processes and G -nonexpansive mappings we refer our readers to see [18][19][20][21].…”