Duality Fixed Point and Zero Point Theorems and Applications
Qingqing Cheng, Yongfu Su, Jingling Zhang · Abstract and Applied Analysis · 2012
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 . 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.