Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems

<p style='text-indent:20px;'>Using the concept of Bregman divergence, we propose a new subgradient extragradient method for approximating common solution pseudo-monotone and Lipschitz continuous variational inequalities fixed point problem in real Hilbert spaces. The algorithm uses self-adjustment rule selecting stepsize each iteration also, prove strong convergence result sequence generated by without prior knowledge constant. Finally, provide some numerical examples to illustrate performance accuracy our finite infinite dimensional spaces.</p>