New Results on Simpson-Type Inequalities for Co-ordinated Convex Function by Generalized Conformable Integrals

Abstract

In this paper, firstly, we prove an identity involving generalized conformable integrals. By using this obtained identity, we establish several Simpson-type inequalities for differentiable co-ordinated convex function by means of generalized conformable fractional integrals. More precisely, some Simpson-type inequalities are obtained using the well-known Hölder and Power mean inequalities. Furthermore, we also consider some special cases which can be deduced from the main results.

KEYWORDS:

• Simpson inequality
• fractional integral operators
• conformable fractional integrals
• co-ordinated convex function

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 26D10
• 26D15
• 26A51
• 26B25

Authors’ contributions

Conceptualization, F.H. and H.B.; investigation, F.H. and H.B.; methodology, F.H.; validation, H.B. and F.H.; visualization, H.B. and F.H.; writing-original draft, F.H.; writing-review and editing, H.B. All authors read and approved the final manuscript.

Disclosure statement

The authors declare that they have no competing interests.

Data availability statement

Data sharing not applicable to this paper as no data sets were generated or analyzed during the current study.

Additional information

Funding

There is no funding.