On the existence of solutions of variational inequalities in Banach spaces

By Jinlu Li. 2004

70 citations recorded by the source corpus.

Abstract In this paper, we study the existence of the solution of the variational inequality 〈Tx−ξ,y−x〉⩾0 by applying the generalized projection operator π K :B ∗ →B , where B is a Banach space with dual space B ∗ and by using the well-known FanKKM Theorem.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/45a2c051ef9aec6907f52c1deeb35b5891708611

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In Computational Theory and Mathematics

1. Nan-Jing Huang
2. Ke-qing Wu
3. Jinlu Li
4. Muhammad Aslam Noor

In Numerical Analysis

1. Nan-Jing Huang
2. Ke-qing Wu
3. Jinlu Li

Citations in the corpus

• The generalized projection operator on reflexive Banach spaces and its applications (2005, methodology): “The following theorem generalizes the main theorem in [16] and [17, Theorem from uniformly convex and uniformly smooth Banach space to reflexive, strictly co and smooth Banach spaces and the mapping is defined only on an arbitrary closed cone.”
• The generalised f -projection operator with an application (2006, methodology): “The metric projection operator PK : B* -> K has been used in many areas such as optimisation theory, fixed point theory, nonlinear programming, game theory, variational inequality, and complementarity problems, et cetera (see, for example, [10, 11, 12, 13, 14, 16, 17, 20] and the references therein)”