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Öğe Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions(De Gruyter Poland Sp Z O O, 2022) Vivas-Cortez, Miguel J. J.; Kara, Hasan; Budak, Hüseyin; Ali, Muhammad Aamir; Chasreechai, SaowaluckIn 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.Öğe Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes(Amer Inst Mathematical Sciences-Aims, 2021) Sitthiwirattham, Thanin; Ali, Muhammad Aamir; Budak, Hüseyin; Chasreechai, SaowaluckIn this paper, we introduce the notions of q-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as q, q(1), q(2) -> 1(-) in the newly obtained results.Öğe Some New Simpson's and Newton's Formulas Type Inequalities for Convex Functions in Quantum Calculus(Mdpi, 2021) Siricharuanun, Pimchana; Erden, Samet; Ali, Muhammad Aamir; Budak, Hüseyin; Chasreechai, Saowaluck; Sitthiwirattham, ThaninIn this paper, using the notions of q(kappa 2)-quantum integral and q(kappa 2)-quantum derivative, we present some new identities that enable us to obtain new quantum Simpson's and quantum Newton's type inequalities for quantum differentiable convex functions. This paper, in particular, generalizes and expands previous findings in the field of quantum and classical integral inequalities obtained by various authors.