Optimality And Duality for Semi-Infinite $$(h,\varphi)-E-convex$$ Programming Problem

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In this paper, a semi-infinite single objective programming problem under $$(h,\varphi)-E-convexity$$ is considered. A new class of function called $$(h,\varphi)-E-convexity$$ function and its generalizations namely pseudo-$$(h,\varphi)-E-convex$$ function and quasi-$$(h,\varphi)-E-convex$$ function is introduced.