On the $$\mathbb {K}$$K-Riemann integral and Hermite–Hadamard inequalities for $$\mathbb {K}$$K-convex functions
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DOI: 10.1007/s00010-017-0472-0
Abstract: In the present paper we introduce a notion of the $$\mathbb {K}$$K-Riemann integral as a natural generalization of a usual Riemann integral and study its properties. The aim of this paper is to extend the… read more here.
Keywords: mathbb riemann; hermite hadamard; riemann integral; hadamard inequalities ... See more keywords
Teaching Integration: How Certain Instructional Moves May Undermine the Potential Conceptual Value of the Riemann Sum and the Riemann Integral
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DOI: 10.1007/s10763-016-9731-0
Abstract: Past research in calculus education has shown that Riemann sum-based conceptions of the definite integral, such as the multiplicatively based summation (MBS) conception, can have important value in interpreting and making sense of certain types… read more here.
Keywords: sum; riemann integral; riemann sum; value ... See more keywords
The Multiple K -Riemann Integral
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DOI: 10.1155/2021/6690328
Abstract: The aim of this paper is to extend the notion of - Riemann integrability of functions defined over to functions defined over a rectangular box of . As a generalization of step functions, we introduce… read more here.
Keywords: riemann integral; multiple riemann;
A Remark on the Change of Variable Theorem for the Riemann Integral
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DOI: 10.3390/math9161899
Abstract: In 1961, Kestelman first proved the change in the variable theorem for the Riemann integral in its modern form. In 1970, Preiss and Uher supplemented his result with the inverse statement. Later, in a number… read more here.
Keywords: change variable; riemann integral; change; theorem riemann ... See more keywords