Related papers: An inequality for completely monotone functions
In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…
We characterize the weighted Hardy's inequalities for monotone functions in ${\mathbb R^n_+}.$ In dimension $n=1$, this recovers the classical theory of $B_p$ weights. For $n>1$, the result was only known for the case $p=1$. In fact, our…
We obtain an interesting inequalities for uniformly continuous functions in the normed spaces: $\|f(x)\|\leq a\|x\|+b$ for some $a,b> 0$.
The paper starts with a concise description of the recently developed semismooth* Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one…
Our aim in this paper is to show some new inequalities for Mathieu's type series and Riemann zeta function. In particular, some Tur\'an type inequalities, some monotonicity and log-convexity results for these special functions are given.…
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain…
In this short note, we improve the famous Reid Inequality related to linear operators.
Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still of great importance, particularly in approximation theory…
We study discrete expressions of the form $$ T_n(g)=\sum_{i=1}^n a_i g(S_i), \qquad S_i=\sum_{j=1}^i a_j, $$ where $a_i>0$ and $\sum_{i=1}^n a_i=1$. If $g:[0,1]\to\mathbb{R}$ is a decreasing integrable function, we have $$ \sum_{i=1}^n a_i…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…
The purpose of this paper is to provide a random version of Simons' inequality.
We give a combinatorial extension of the classical inequalities of Maclaurin about symmetric functions of several variables. We discuss two problems - one analytical and another combinatorial - and show that they are in some sense…
In this note we use recent results concerning the sum theorem for maximal monotone multifunctions in general Banach spaces to find new characterizations and properties of regular maximal monotone multifunctions and then use these to…
The estimate in Bullen's inequality will be extended for continuous functions using the second order modulus of smoothness. A different form of this inequality will be given in terms of the least concave majorant. Also, the composite case…
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
In this paper, we first establish a version of multidimensional analogues of the refined Bohr's inequality. Then we establish two versions of multidimensional analogues of improved Bohr's inequality with initial coefficient being zero.…
In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method…
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.