Mixed quasi invex equilibrium problems
We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204310112 |
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| Summary: | We introduce a new class of equilibrium problems, known as
mixed quasi invex equilibrium (or
equilibrium-like) problems. This class of invex
equilibrium problems includes equilibrium
problems, variational inequalities, and
variational-like inequalities as special cases. Several iterative
schemes for solving invex equilibrium problems are suggested and
analyzed using the auxiliary principle technique. It is shown
that the convergence of these iterative schemes requires either
pseudomonotonicity or partially relaxed strong monotonicity,
which are weaker conditions than the previous ones. As special
cases, we also obtained the correct forms of the algorithms for
solving variational-like inequalities, which have been considered
in the setting of convexity. In fact, our results represent
significant and important refinements of the previously known
results. |
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| ISSN: | 0161-1712 1687-0425 |