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Let
be a Banach space and let
be the unit sphere of
...
We give some necessary and sufficient conditions for the class of Appell polynomials to satisfy well-known Turan's inequality. Among the other corollaries, we apply our results to some classes of orthogonal po...
Picone-type inequalities are established for nonlinear elliptic equations which are generalizations of nonself-adjoint linear elliptic equations, and Sturmian comparison theorems are derived as applications. O...
We establish upper bounds for the eigenvalues of second-order and fourth-order differential equations. The inequalities are obtained via rearrangements of higher degree.
We consider a model of economic dynamics with discrete innovations and establish the existence of trajectories with unbounded consumption.
We prove the following let
, and
be real numbers, and let
...
A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of hal...
For one class of hyperbolic systems of second order, we consider multidimensional versions of the Darboux problem in conic domains. A priori estimates of solutions of these problems are obtained. The existence...
We prove that the projection operator on a nonempty closed convex subset
of a uniformly convex Banach spaces is uniformly continuous on bounded ...
We improve several results recently established by Dragomir et al. in (2000) for the Gamma and Beta functions. All we need is some clever applications of classical inequalities.
We investigate the existence of continuous solutions on compact intervals of some nonlinear integral equations. The existence of such solutions is based on some well-known fixed point theorems in Banach spaces...
This paper deals with the problem of estimating the deviation of the values of a function from its mean value. We consider the following special cases: (i) the case of random variables (attached to arbitrary p...
Using inequalities for a certain function appearing in the half-linear version of Picone's identity, we show that oscillatory properties of the half-linear second-order differential equation ...
We analyze the univalence of the solutions of the biharmonic equation. In particular, we show that if
is a biharmonic map in the form
Let
be a measurable function defined on the unit polydisc
in
We deal with a theoric question raised in connection with the application of a three-critical points theorem, obtained by Ricceri, which has been already applied to obtain multiplicity results for boundary val...
Some matrix versions of the Cauchy-Schwarz and Frucht-Kantorovich inequalities are established over the quaternionic algebra. As applications, a group of inequalities for sums of Hermitian nonnegative definite...
The purpose of this paper is to introduce the concept of fuzzy variational-like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy v...
Using the notion of inferior mean due to M. Heins, we establish two inequalities for such a mean relative to a positive harmonic function defined on the open unit ball or half-space in ...
This study focuses on anisotropic Sobolev type spaces associated with Banach spaces
,
We study the first boundary value problem for a class of nonlinear degenerate parabolic equations
. We first consider its regularized problem and...
We consider the following system of differential equations
,
,
We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias s...
Let
be a normed linear space,
an element of norm one, and
...
Some new Gronwall-Ou-Iang type integral inequalities in two independent variables are established. These integral inequalities can be applied as tools to the study of certain class of integral and differential...
We consider
and a corresponding geometric mean operator
. E. T. Sawyer showed...
for some weighted algebraic and trigonometric polynomials
Bernstein inequalities are given for polynomials of degree at most
(where
), ...
We apply a fixed point result for multifunctions to derive existence results for boundary value problems of Sturm-Liouville differential equations with nonlinearities that may involve discontinuous and functio...
We give a Grüss-type inequality which is a refinement of a result due to Dragomir and Agarwal. We also give its applications for the moments of random variables, guessing mappings, and Ozeki's inequality.
We introduce and study a new class of generalized nonlinear implicit quasivariational inclusions involving relaxed Lipschitzian mappings. We prove the existence of solution for the generalized nonlinear implic...
By use of the concavity of solution for an associate boundary value problem, existence criteria of positive solutions are given for the Dirichlet BVP
Let
be a strictly increasing sequence of natural numbers and let
be a space ...
We introduce and study a new class of generalized nonlinear variational-like inequalities, which includes these variational inequalities and variational-like inequalities due to Bose, Cubiotti, Dien, Ding, Din...
One-dimensional Hardy inequalities with weights and remainder terms are studied. The corresponding optimal constants are discussed. Then by the process of symmetrization, Hardy inequalities with remainder term...
The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. W...
We establish optimal, in a sense, unique solvability conditions of the Cauchy problem for a wide class of linear functional differential equations in a Banach space with a solid wedge. The conditions are formu...
We study Carrier's equation in a noncylindrical domain. We use the penalty method combined with Faedo-Galerkin and compactness arguments. We obtain results of the existence and uniqueness of the local solution.
We consider a natural correspondence between a family of inequalities and a closed convex set. As an application, we give new types of power mean inequalities and the Hölder-type inequalities.
We first prove local weighted Poincaré-type inequalities for differential forms. Then, by using the local results, we prove global weighted Poincaré-type inequalities for differential forms in John domains, wh...
For the linear delay difference system
, where
is a
...
We investigate the global asymptotic behavior of solutions of the system of difference equations
,
...
The classical Bernstein pointwise estimate of the (first) derivative of a univariate algebraic polynomial on an interval has natural extensions to the multivariate setting. However, in several variables the do...
We prove some common fixed point theorems for left reversible and near-commutative semigroups in compact and complete metric spaces, respectively. As applications, we get the existence and uniqueness of soluti...
The well-known Krasnoselskii twin fixed point theorem is used to investigate the existence of mild solutions for first- and second-order impulsive semilinear functional and neutral functional differential equa...
A general method is given in order to guarantee at least one nontrivial solution, as well as infinitely many radially symmetric solutions, for an abstract class of hemivariational inequalities. This abstract c...
We develop an inequality for the expectation of a product of
random variables generalizing the recent work of Dedecker and Doukhan (2003) and th...
The new extension of the weighted Montgomery identity is given by using Fink identity and is used to obtain some Ostrowski-type inequalities and estimations of the difference of two integral means.
Let
denote the space of all holomorphic functions on the unit ball
. In this ...
We give a refinement of the Poincaré inequality for Kolmogorov operators on
. This refinement yields some regularity result of the corresponding ...
The inequality discovered by L. K. Hua in 1965 has been generalized in several directions. In this paper, we adopt a certain conjugate method to give a simple and fundamental inequality on two functions on a s...
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