Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

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Vivas-Cortez M. J. J., Kara H., Budak H., Ali M. A., Chasreechai S.

OPEN MATHEMATICS, no.1, pp.1887-1903, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1515/math-2022-0477
  • Journal Name: OPEN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.1887-1903
  • Kocaeli University Affiliated: No

Abstract

In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.