Journal of innovative applied mathematics and computational sciences
Volume 2, Numéro 2, Pages 48-52
2022-09-10
Results In Semi-e-convex Functions
Authors : Benhadid Ayache .
Abstract
The concept of convexity and its various generalizations is important for quantitative and qualitative studies in operations research or applied mathematics. Recently, E-convex sets and functions were introduced with important implications across numerous branches of mathematics. By relaxing the definition of convex sets and functions, a new concept of semi-EE-convex functions was introduced, and its properties are discussed. It has been demonstrated that if a function f:M→Rf:M→R is semi-EE-convex on an EE-convex set M⊂RnM⊂Rn then, f(E(x))≤f(x)f(E(x))≤f(x) for each x∈Mx∈M. This article discusses the inverse of this proposition and presents some results for convex functions.
Keywords
Semi-E-convex functions, convex functions, Lower semi-continuous functions
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