Abstract
In this paper, we introduce and investigate a new class of generalized convex functions, called generalized geometrically r-convex functions. Some new Hermite-Hadamard integral inequalities via generalized geometrically r-convex functions have been established. Results proved in this paper can be viewed as new significant contributions in this area of research.
Highlights
Several branches of mathematical and engineering sciences has been developed by using the crucial and significant concepts of convex analysis and it becomes one of the most interesting and useful concept of mathematics for last few decades
We introduce and investigate a new class of generalized convex functions, called generalized geometrically r-convex functions
First aspect is concerned with differentiable convex functions
Summary
Several branches of mathematical and engineering sciences has been developed by using the crucial and significant concepts of convex analysis and it becomes one of the most interesting and useful concept of mathematics for last few decades. Generalized convex functions; generalized geometrically r-convex functions; Hermite-Hadamard type inequalities. Several authors have derived Hermite-Hadamard type inequalities for various classes of r-convex functions, see [22, 28, 31,32,33]. Gordji et al [9] introduced an important class of convex functions involving the bifunction, which is called generalized(φ-convex) convex function. Using the technique and ideas of this paper, one may obtain HermiteHadamard type integral inequalities for other classes of convex functions and their variant forms. A function f : I ⊂ R+ =(0,∞)→ R is said to be geometrically convex, if f (a1−tbt) ≤ (1 − t)f (a) + t(f (b)), ∀a, b ∈ I, t ∈ [0, 1], We define a new concept of generalized geometrically r-convex functions.
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