@article{article_484452, title={A generalized nonlinear iterative algorithm for the explicit midpoint rule of nonexpansive semigroup}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={69}, pages={613–628}, year={2020}, DOI={10.31801/cfsuasmas.484452}, author={Sahebi, Hamid Reza and Azhını, Mahdi and Cheraghi, Masume}, keywords={Nonexpansive semigroup,equilibrium problem,midpoint method,strongly positive linear bounded operator}, abstract={<p>In this paper, we introduce a new iterative midpoint rule for finding a solution of xed point problem for a nonexpansive semigroup in real Hilbert spaces. We establish a strong convergence theorem for the sequences generated by our proposed iterative scheme. Furthermore, we provide application to Fredholm integral equations. A <br />numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature. <br /> </p>}, number={1}, publisher={Ankara University}