Abstract
In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is provided. The authors also prove an identity for twice q - differentiable functions using Raina’s function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.
Highlights
The convexity of a function has played a very important role as a tool in the development of inequalities
The famous Hermite–Hadamard inequality, which involves convex functions, appears in the literature regarding the study of inequalities
In [10], Noor M.A. introduced a new class of non-convex functions, the so-called φ-convex, as follows: Definition 2
Summary
The convexity of a function has played a very important role as a tool in the development of inequalities. The relationship of this concept is always present in branches such as functional analysis [1], harmonic analysis ( in interpolation theory) [2] and control theory and optimization [3]. Motivated by the growing body of work on the development of the concept of convexity, its relationships with integral inequalities and its connection with quantum analysis, as is addressed in the work mentioned above, in this work we seek to establish certain quantum estimates of trapezium-type inequalities for generalized φ-convex functions
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