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In this article, we present semi strongly $E$-preinvexity and semi strongly$E$-invexity. To demonstrate the existence of these functions, certainnontrivial examples have been developed. Several significant relationships andcharacterizations of these functions on strongly $E$-invex sets are discussed.Furthermore, we consider a non-linear programming problem for semi strongly$E$-preinvex functions and investigate relationships between the set of optimalsolutions and these functions.

Non-linear programming problem for semi strongly $E$-preinvexity