On generalization of E-convex and composite functions. Issue 6 (18th August 2021)

• Record Type: Journal Article
• Authors: Nanda, Sudarsan
• Is Part Of: Journal of information & optimization sciences. Volume 42:Issue 6(2021)
• Page Start: 1271
• Page End: 1282
• Publication Date: 2021-08-18
• Subjects: 90C30; E-convex set -- E-convex function -- Linear operator -- Generalized E-convex function -- Affine function -- Convex -- Quasi convex; Electronic data processing -- Periodicals; Information science -- Periodicals; Mathematical optimization -- Periodicals; 519.6
• DOI: 10.1080/02522667.2020.1868660
• Languages: English
• ISSNs: 0252-2667

Abstract

Abstract: In this paper the concepts of some generalizations of E-convexity such as logarithmic, and exponential E-convexity are introduced for real-valued functions defined on a Banach space and their relationships with known concepts have been discussed. Further, some applications to optimization of non-differentiable objective functions have been proposed. Also, it is proved that the composition of an affine and a G-convex functional is G-convex, where G stands for convex, quasi-convex, r-quasi convex and m-quasi convex.