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EN
In this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite-Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space Rn for any n ≥ 2.
2
Content available remote Ulam-Hyers stability of a parabolic partial differential equation
EN
The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. Some examples are given, one of them being the Black-Scholes equation.
EN
In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.
4
Content available remote On an inequality of the Lupas type
EN
An inequality of the Lupas, type for Cebysev functionals is established.
5
Content available remote Notes on integral inequalities
EN
New results, generalizations and improvements concerning several integral inequalities are obtained.
6
Content available remote Integral inequalities on infinite intervals
EN
Inequalities concerning the distance between a function and some integrals on infinite intervals are given.
7
Content available remote A note on new integral inequalities of Gruss type
EN
The aim of this note is to establish two new Gruss type integral inequalities involving functions and their derivatives by using a fairly elementary analysis.
EN
Let alphis an element of [0,1]. A function f :I -> R (0 is an element of I) is said to be alpha-star-convex on [...]. In this note we will present new geometric interpretation of alpha-star-convex functions and some Hadamards' like integral inequalities for such functions.
PL
W pracy przeprowadza się analizę klasy funkcji spełniających pewne kwadratowe nierówności całkowe drugiego rzędu w zależności od wartości granicznych pewnych funkcji.
EN
In the paper the classes of functions fulfilling some quadratic integral inequalities of the second order are described on limit values of some functions.
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