Main Article Content
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.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
- Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
X. Chen, Some properties of semi-E-convex functions, J. Math. Anal. Appl., 275 (2002), 251–262.
G. Dal maso, An Introduction to G-convergence, BirKhauser, Boston, 1993.
A. A. Megahed, H. G. Gomma, E. A. Youness and A. H. Banna, Optimality conditions of E-convex programming for an E-differentiable function, J. Inequal. Appl., 246 (2013), 1–11.
M. A. Noor, M. U. Awan and K. I. Noor, On some inequalities for relative semi-convex functions, J. Inequal. Appl., 332 (2013), 1–16.
E. A. Youness, E-convex sets, E-convex functions, and E-convex programming, J. Optim. Theory Appl., 102 (1999), 439–450.