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Bregman f‐Projection Operator with Applications to Variational Inequalities in Banach Spaces

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  • Chin-Tzong Pang
  • Eskandar Naraghirad
  • Ching-Feng Wen

Abstract

Using Bregman functions, we introduce the new concept of Bregman generalized f‐projection operator ProjCf, g:E*→C, where E is a reflexive Banach space with dual space E*; f : E → ℝ ∪ {+∞} is a proper, convex, lower semicontinuous and bounded from below function; g : E → ℝ is a strictly convex and Gâteaux differentiable function; and C is a nonempty, closed, and convex subset of E. The existence of a solution for a class of variational inequalities in Banach spaces is presented.

Suggested Citation

  • Chin-Tzong Pang & Eskandar Naraghirad & Ching-Feng Wen, 2014. "Bregman f‐Projection Operator with Applications to Variational Inequalities in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:594285
    DOI: 10.1155/2014/594285
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    References listed on IDEAS

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    1. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, March.
    2. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
    3. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-39, February.
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