Related papers: Some inequalities for interval-valued functions on…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…
We study the function $\Delta_k(x):=\sum_{n\leq x} d_k(n) - \mbox{Res}_{s=1} ( \zeta^k(s) x^s/s )$, where $k\geq 3$ is an integer, $d_k(n)$ is the $k$-fold divisor function, and $\zeta(s)$ is the Riemann zeta-function. For a large parameter…
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.
We know that a continuous function on a closed interval satisfies the Intermediate Value Property. Likewise, the derivative function of a differentiable function on a closed interval satisfies the IVP property which is known as the Darboux…
In this paper, the author establishes some Hadamard-type and Bullen-type inequalities for Lipschitzian functions via Riemann Liouville fractional integral. These results have some relationships with [K.-L. Tseng, S.-R. Hwang and K.-C. Hsu,…
We study the \lq \lq symmetry integral\rq \rq, \thinspace say $I_f$, of some arithmetic functions $f:\N \rightarrow \R$; we obtain from lower bounds of $I_f$ (for a large class of arithmetic functions $f$) lower bounds for the \lq \lq…
In this paper, we establish some integral ineuqalities for n- times differentiable convex functions.
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
Several results are obtained concerning the function $\Delta_k(x)$, which represents the error term in the general Dirichlet divisor problem. These include the estimates for the integral of this function, as well as for the corresponding…
Let $\Delta(x)$ denote the error term in the Dirichlet divisor problem. Our main results are the asymptotic formulas $$ \int_1^X \Delta^3(x){\rm d}x = BX^{7/4} + O_\epsilon(X^{\beta+\epsilon}) \qquad(B > 0) $$ and $$ \int_1^X…
Let $\Delta(x)$ be the error term of the Dirichlet divisor problem. The asymptotic formula of the integral $\int_1^T\Delta^k(x)dx$ is established for any integer $3\leq k\leq 9$ by an unified method. Similar results are also established for…
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
In this article, we introduce the interval optimization problems (IOPs) on Hadamard manifolds as well as study the relationship between them and the interval variational inequalities. To achieve the theoretical results, we build up some new…
We introduce the forward (backward) gH-difference operator of interval sequences, and establish some new discrete Opial type inequalities for interval-valued functions. Further, we obtain generalizations of classical discrete Opial type…
We formulate and discuss integrable analogue of the sine-Gordon equation on arbitrary time scales. This unification contains the sine-Gordon equation, discrete sine-Gordon equation and the Hirota equation (doubly discrete sine-Gordon…
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann-Liouville sense. We also introduce the nabla fractional derivative in Gr\"unwald-Letnikov sense. Some of the basic properties…
We generalize aspects of Fourier Analysis from intervals on $\mathbb{R}$ to bounded and measurable subsets of $\mathbb{R}^n$. In doing so, we obtain a few interesting results. The first is a new proof of the famous Integral Cauchy-Schwarz…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.