MinLimit

MinLimit[f,x->x*] gives the min limit x->x*f(x). 

MinLimit[f,{x1->x1*,…,xn->xn*}] gives the nested min limit +x1->x1*⋯ +xn->xn*f(x1,…,xn). 

MinLimit[f,{x1,…,xn}->{x1*,…,xn*}] gives the multivariate min limit +{x1,…,xn}->{x1*,…,xn*}f(x1,…,xn).

Please visit the official Wolfram Language Reference for more details and examples on core symbols.