Adaptive double-inertial projection rules for variational inequalities and CFPPs of finite Bregman relative demicontractions and asymptotical nonexpansivity operators

Presume the uniform smooth Banach space $E$ to possess $p$-uniform convexity for $p\ge 2$. In $E$, the VIP stands for a variational inequality problem and the CFPP a common fixed point problem of Bregman’s relative asymptotic nonexpansivity operator and finite Bregman’s relative demicontractions. We design and deliberate two adaptive double-inertial Bregman’s projection schemes with linesearch procedure for tackling the CFPP and a pair of VIPs. Through appropriate postulations, it is substantiated that the generated sequences in the proposed schemes, are weakly and strongly convergent to a common solution of the CFPP and two VIPs, respectively. At length, an illustration is offered to substantiate the utility and performability of the schemes put forward.