Existence results and gap functions for the generalized equilibrium problem with composed functions |
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Authors: | Radu Ioan Bo? Adela Elisabeta Cap?t? |
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Institution: | a Faculty of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany b Faculty of Mathematics and Computer Science, Babe?-Bolyai University, Cluj-Napoca, Romania |
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Abstract: | In this paper we provide first existence results for solutions of the generalized equilibrium problem with composed functions (GEPC) under generalized convexity assumptions. Then we construct by employing some tools specific to the theory of conjugate duality two gap functions for (GEPC). The importance of these gap functions is to be seen in the fact that they equivalently characterize the solutions of an equilibrium problem. We also prove that for some particular instances of (GEPC) the gap functions we introduce here become among others the celebrated Auslender’s and Giannessi’s gap functions. |
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Keywords: | 49J10 49N15 90C25 |
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