Modified Krasnoselski–Mann type iterative algorithm with strong convergence for hierarchical fixed point problem and split monotone variational inclusions

Accelerated Krasnoselski-Mann type algorithm for hierarchical fixed point and split monotone variational inclusion problems in Hilbert spaces

“…(e) the result improved the corresponding ones in D.-J. Wen [31] and K.P. Kim and K. Majee [19], in the sense that it solves some fixed point problem of demimetric mapping in addition to HFPP and SMVIP with faster rate of convergence;…”

“…Very recently, D.-J. Wen [31] modified algorithm (7) by replacing the nonexpansive self mapping T with (1 − µ n D) and prove that the sequence {x n } iteratively generated by…”

“…Kim and K. Majee [19] and D.-J. Wen [31], we introduce a new accelerated extrapolation Krasnoselski-Mann type algorithm (see algorithm 1 below) for finding common element in the solution set of the HFPP and SMVIP which also approximates some solution of fixed point problem of demimetric mapping in the setting of real Hilbert spaces. In respect to this, the following motivations that signify the contributions of our proposed method (algorithm) are highlighted:…”

A modified forward‐backward splitting methods for the sum of two monotone operators with applications to breast cancer prediction

“…The fast iterative shrinkage-thresholding algorithm (FISTA) 17 is very usefull because it's easy to compute and it has a better convergence rate than the standard forward-backward algorithm. 12,[18][19][20][21][22] The algorithm is designed by choosing…”

“…Many inertial technique types have been modified for algorithm construction solving the problem CMP (). The fast iterative shrinkage‐thresholding algorithm (FISTA) 17 is very usefull because it's easy to compute and it has a better convergence rate than the standard forward‐backward algorithm 12,18–22 . The algorithm is designed by choosing $$$ {s}^1={t}^0\in H,{c}^1=1,\gamma >0 $$$ and compute $$$$ \left\{\begin{array}{c}{t}^k= pro{x}_{\gamma g}\left({s}^k-\gamma \nabla f{s}^k\right),\\ {}{c}^{k+1}=\frac{1+\sqrt{1+4{\left({c}^k\right)}^2}}{2},\\ {}{\theta}^k=\frac{c^k-1}{c^{k+1}},\\ {}{s}^{k+1}={t}^k+{\theta}^k\left({t}^k-{t}^{k-1}\right).\end{array}\right.$$…”