In this paper, we introduce the h-convex concept for interval-valued functions. By using the h-convex concept, we present new Jensen and Hermite-Hadamard type inequalities for interval-valued functions. Our inequalities generalize some known results.
In this work, we introduce the notion of interval-valued coordinated convexity and demonstrate Hermite–Hadamard type inequalities for interval-valued convex functions on the co-ordinates in a rectangle from the plane. Moreover, we prove Hermite–Hadamard inequalities for the product of interval-valued convex functions on coordinates. Our results generalize several other well-known inequalities given in the existing literature on this subject.
In this paper, we introduce and investigate the concepts of conformable delta fractional derivative and conformable delta fractional integral on time scales. Basic properties of the theory are proved.
In this paper, we establish Hermite-Hadamard inequality for interval-valued convex function on the co-ordinates on the rectangle from the plane. We also present Hermite-Hadamard inequality for the product of interval-valued convex functions on co-ordinates. Some examples are also given to clarify our new results.For more results related to (1.2) we refer ( [1], [10], [16]) and references therein. On the other hand, interval analysis is a particular case of set-valued analysis which is the study of sets in the spirit of mathematical analysis and general topology. It was introduced as an attempt to handle interval uncertainty that appears in many mathematical or computer models of some deterministic real-world phenomena. An old example of interval enclosure is Archimede's method which is related to compute of the circumference of a circle. In 1966, the first book related to interval analysis
We introduce the concept of interval ( h 1 , h 2 ) -convex functions. Under the new concept, we establish some new interval Hermite-Hadamard type inequalities, which generalize those in the literature. Also, we give some interesting examples.
We introduce the concept of interval harmonically convex functions. By using two different classes of convexity, we get some further refinements for interval fractional Hermite-Hadamard type inequalities. Also, some examples are presented.
MSC: 26D15; 26E25; 26A33
We introduce the interval Darboux delta integral (shortly, the ID ∆-integral) and the interval Riemann delta integral (shortly, the IR ∆-integral) for interval-valued functions on time scales. Fundamental properties of ID and IR ∆-integrals and examples are given. Finally, we prove Jensen's, Hölder's and Minkowski's inequalities for the IR ∆-integral. Also, some examples are given to illustrate our theorems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.