Duality Fixed Point and Zero Point Theorems and Applications

The following main results have been given. (1) Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1)-L-Lipschitz mapping with condition 0<(pL/c2)1/(p-1)<1. Then T has a unique generalized duality fixed point x*∈E and (2) let E be a p-uniformly convex Banach space and let T:E→E* be a q-α-inverse strongly monotone mapping with conditions 1/p+1/q=1, 0<(q/(q-1)c2)q-1<α. Then T has a unique generalized duality fixed point x*∈E. (3) Let E be a 2-uniformly smooth and uniformly convex Banach space with uniformly convex constant c and uniformly smooth constant b and let T:E→E* be a L-lipschitz mapping with condition 0<2b/c2<1. Then T has a unique zero point x*. These main results can be used for solving the relative variational inequalities and optimal problems and operator equations