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$Iq$-Hermite-Hadamard inclusions for the interval-valued functions of two variables
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  • Muhammad Aamir Ali,
  • Hüseyin BUDAK,
  • Hasan Kara,
  • Shahid Qaisar
Muhammad Aamir Ali
Nanjing Normal University School of Mathematical Sciences
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Hüseyin BUDAK
Düzce University
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Hasan Kara
Düzce Üniversitesi
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Shahid Qaisar
COMSATS, Institute of information technology, Islamabad, Sahiwal Campus
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Abstract

In this work, we introduce the concept of double quantum integrals for the interval-valued functions of two variables. We offer several new inclusions of the Hermite-Hadamard type for co-ordinated convex interval-valued functions using the newly defined integrals. Moreover, we prove trapezoidal type inequalities for interval-valued functions of two variables using the ideas of the Pompeiu--Hausdorff distance between the intervals. It is also revealed that the results offered in this work are the generalization of several existing results.

Peer review status:UNDER REVIEW

21 Sep 2020Submitted to Mathematical Methods in the Applied Sciences
22 Sep 2020Assigned to Editor
22 Sep 2020Submission Checks Completed
31 Dec 2020Review(s) Completed, Editorial Evaluation Pending
04 Jun 2021Reviewer(s) Assigned