Abstract
In this paper, bounds of fractional and conformable integral operators are established in a compact form. By using exponentially convex functions, certain bounds of these operators are derived and further used to prove their boundedness and continuity. A modulus inequality is established for a differentiable function whose derivative in absolute value is exponentially convex. Upper and lower bounds of these operators are obtained in the form of a Hadamard inequality. Some particular cases of main results are also studied.
Highlights
We start with the definition of convex function.Definition 1
Our goal in this paper is to prove generalized integral inequalities for exponentially convex functions by using integral operators given in Definition 7
(x) If we consider φ(t) tμ/kFσρ,λk(w(t)ρ), (11) and (12) produce generalized k-fractional integral operators defined by Tunc et al in [25]
Summary
We start with the definition of convex function. Definition 1 (see [1]). Our goal in this paper is to prove generalized integral inequalities for exponentially convex functions by using integral operators given in Definition 7. E leftsided and right-sided k-fractional integral operators, k > 0, of a function f with respect to another function g on [a, b] of order μ, k ∈ C, R(μ) > 0 are defined by μ g. (iii) If we consider φ(t) (tμ/k/kΓk(μ)) and g as identity function (11) and (12), integral operators coincide with (5 and 6) fractional integral operators. (x) If we consider φ(t) tμ/kFσρ,,λk(w(t)ρ), (11) and (12) produce generalized k-fractional integral operators defined by Tunc et al in [25]. We will derive bounds of sum of the left- and right-sided integral operators defined in (11) and (12) for exponentially convex functions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
