G-pre-invex functions in mathematical programming |
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Authors: | Tadeusz Antczak |
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Institution: | aFaculty of Mathematics and Informatics, University of Łódź, Banacha 22, 90-238 Łódź, Poland |
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Abstract: | In the present paper, we introduce the concept of G-pre-invex functions with respect to η defined on an invex set with respect to η. These function unify the concepts of nondifferentiable convexity, pre-invexity and r-pre-invexity. Furthermore, relationships of G-pre-invex functions to various introduced earlier pre-invexity concepts are also discussed. Some (geometric) properties of this class of functions are also derived. Finally, optimality results are established for optimization problems under appropriate G-pre-invexity conditions. |
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Keywords: | G-pre-invex function with respect to η Invex set with respect to η G-invex set with respect to η Optimality |
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