Duality Fixed Point and Zero Point Theorems and Applications

Qingqing Cheng, Yongfu Su and Jingling Zhang

Abstract and Applied Analysis, 2012, vol. 2012, 1-11

Abstract:

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 < ( p L / c 2 ) 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 ) c 2 ) 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 < 2 b / c 2 < 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.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2012/391301.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2012/391301.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:391301

DOI: 10.1155/2012/391301

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().