Semi E<sup>h</sup>-b-preinvexity and its applications to optimization problems
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Abstract<p>In this paper, the class of semi <italic>E</italic>
<sup>
<italic>h</italic>
</sup>-<italic>b</italic>-preinvex and pseudo <italic>E</italic>
<sup>
<italic>h</italic>
</sup>-b-preinvex functions are defined as an extension of <italic>E-B</italic>-preinvex and <italic>h</italic>-preinvex functions. In this extension the functions <italic>E</italic>:ℝ<sup>
<italic>n</italic>
</sup> → ℝ<sup>
<italic>n</italic>
</sup>, <italic>h</italic>: [0,1] → ℝ, and <italic>b</italic>:ℝ<sup>
<italic>n</italic>
</sup> × ℝ<sup>
<italic>n</italic>
</sup> × [0,1] → ℝ<sup>+</sup> are taken into consideration. Various properties for the new functions as well as some properties and characterizations of quasi semi <italic>E</italic>-preinvex functions are discussed. Some optimality properties for semi <italic>E</italic>
<sup>
<italic>h</italic>
</sup>-b-preinvex nonlinear optimization problems are proved.</p>
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