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Generalized fractional midpoint type inequalities for co-ordinated convex functions
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  • Fatih HEZENCİ,
  • Hüseyin BUDAK,
  • Hasan KARA,
  • Mehmet Zeki Sarikaya
Düzce Üniversitesi
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Hüseyin BUDAK
Duzce University
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Hasan KARA
Düzce Üniversitesi
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Mehmet Zeki Sarikaya
Duzce Universitesi
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In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for $k$-Riemann-Liouville fractional integrals are presented as special cases of our results.

Peer review status:UNDER REVIEW

12 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
14 Nov 2021Assigned to Editor
14 Nov 2021Submission Checks Completed
19 Nov 2021Reviewer(s) Assigned