Abstract
The authors have proved an identity for a generalized integral operator via differentiable function. By applying the established identity, the generalized trapezium type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results have been analyzed.
Highlights
The authors have proved an identity for a generalized integral operator via differentiable function
It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades
It is important to summarize the study of fractional integrals as follow: Definition 1.2
Summary
Let f : I ⊆ R −→ R be convex, a1, a2 ∈ I and a1 < a2. Authors of recent decades have studied (1.1) in the premises of newly invented definitions due to motivation of convex function. It is important to summarize the study of fractional integrals as follow: Definition 1.2. K-fractional integrals of order α, k > 0, where a1 ≥ 0 is given as. The left-sided and rightsided generalized integral operators are defined as follows:. For other feature of generalized integrals, see [14]. The main objective of this paper is to discover, an interesting identity in order to study some new bounds regarding trapezium type integral inequalities. By using the established identity as an auxiliary result, some new estimates for trapezoidal type integral inequalities via generalized integrals are obtained. A briefly conclusion is provided as well
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