Title

Exceptional family of elements and solvability of variational inequalities for mappings defined only on closed convex cones in Banach spaces

Document Type

Article

Publication Date

3-10-2005

Original Publication Title

Journal of Mathematical Analysis and Applications

Department

Mathematical Sciences

DOI

https://doi.org/10.1016/j.jmaa.2005.02.006

Abstract

In this paper, we generalize the concept of exceptional family of elements for a completely continuous field from Hilbert spaces to Banach spaces and we study the solvability of the variational inequalities with respect to a mapping f that is from a closed convex cone of a Banach space B to the dual space B∗" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">B∗ by applying the generalized projection operator πK" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">πK and by using the Leray–Schauder type alternative.

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