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Duality Fixed Point and Zero Point Theorems and Applications

Author

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  • Qingqing Cheng
  • Yongfu Su
  • Jingling Zhang

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.

Suggested Citation

  • Qingqing Cheng & Yongfu Su & Jingling Zhang, 2012. "Duality Fixed Point and Zero Point Theorems and Applications," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, September.
    • Handle: RePEc:hin:jnlaaa:391301
    DOI: 10.1155/2012/391301
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