Duality Fixed Point and Zero Point Theorems and Applications

Abstract

The following main results have been given. (1) LetEbe ap-uniformly convex Banach space and letT:E→E*be a(p-1)-L-Lipschitz mapping with condition0<(pL/c2)1/(p-1)<1. ThenThas a unique generalized duality fixed pointx*∈Eand (2) letEbe ap-uniformly convex Banach space and letT:E→E*be aq-α-inverse strongly monotone mapping with conditions1/p+1/q=1,0<(q/(q-1)c2)q-1<α. ThenThas a unique generalized duality fixed pointx*∈E. (3) LetEbe a2-uniformly smooth and uniformly convex Banach space with uniformly convex constantcand uniformly smooth constantband letT:E→E*be aL-lipschitz mapping with condition0<2b/c2<1. ThenThas a unique zero pointx*. These main results can be used for solving the relative variational inequalities and optimal problems and operator equations.