Abstract
Convexity plays an important role in many areas of mathematics, especially in the study of optimization problems where they are distinguished by a number of convenient properties. Our aim is to introduce a more extended version of convexity. In this paper, we introduced interval-valued generalized η h convex function and proved Hermite–Hadamard-, Jensen-, and Ostrowski-type inequalities in this generalization. The presented results are generalizations of many existing results of literature.
Highlights
It is always interesting and appreciable to generalize the definition of convexity from different aspects because it helps to tackle modern world problem. e famous generalizations of convexity are E-convex functions [1], α convex functions [2], φ-convex function [3], and convex vector [4]
We introduced ηh generalized convex function over interval-valued setting and proved Hermite–Hadamard, Jensen, and Ostrowski-type inequalities
Let f1, g1: J1 ⟶ R are two generalized ηh convex functions. en, the following statements hold: (1) If η is additive, f1 + g1: J1 ⟶ R is generalized ηh convex
Summary
In nonlinear programming and optimization theory, convexity plays an important role. Ere were three important areas of nonlinear analysis: monotone operator theory, convex analysis, and theory of nonexpensive mapping, but in early 1960, these theories get emerged. Ese areas got the attention of many researchers, and many connections have been identified between them over the past few years. It is always interesting and appreciable to generalize the definition of convexity from different aspects because it helps to tackle modern world problem. E famous generalizations of convexity are E-convex functions [1], α convex functions [2], φ-convex function [3], and convex vector [4]. Consider a convex function f1: J1⊆R ⟶ R, the following inequality holds: f1x1 + 2 y1 ≤ y1 1 − x1 f1(x)dx f1 It is always interesting and appreciable to generalize the definition of convexity from different aspects because it helps to tackle modern world problem. e famous generalizations of convexity are E-convex functions [1], α convex functions [2], φ-convex function [3], and convex vector [4].
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