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Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are d...
-Laplacian
We deal with discontinuous quasilinear elliptic variational-hemivariational inequalities. By using the method of sub- and supersolutions and based on the results of S. Carl, we extend the theory for discontinu...
In this note, new upper bounds for Carleman's inequality and Hardy's inequality are established.
The purpose of this paper is to investigate some nonlinear integral inequalities on time scales. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. The theore...
We obtain the general solution and the stability of the
-variable quadratic functional equation
...
We investigate when a natural iterative method converges to the exact solution of a differential-functional von Foerster-type equation which describes a single population depending on its past time and state d...
The difference sequence space
, which is a generalization of the space
We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation.
We generalize the notions of Levitin-Polyak well-posedness to an equilibrium problem with both abstract and functional constraints. We introduce several types of (generalized) Levitin-Polyak well-posedness. So...
Using quadrature formulae of the Gauss-Lobatto type, we give some new results for extremal problems with polynomials.
In 2007, Ozden et al. constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic, q-deformed fermionic integral on ...
Variables
We establish Schur-convexities of two types of one-parameter mean values in
variables. As applications, Schur-convexities of some well-k...
By using Lyapunov functions and Razumikhin techniques, the strict stability of impulsive functional differential systems is investigated. Some comparison theorems are given by virtue of differential inequaliti...
Starting out from a question posed by T. Erdélyi and J. Szabados, we consider Schur-type inequalities for the classes of complex algebraic polynomials having no zeros within the unit disk ...
This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield some of the recent results and provide some new estimates on such types of inequalities.
We give John-Nirenberg type inequalities for the Morrey-Campanato spaces on
.
Let
be a real Hilbert space,
a nonempty closed convex subset of
-Laplacian Equations with Exponential Nonlinearities
This paper investigates the
-Laplacian equations with exponential nonlinearities
...
We show that the general variational inequalities are equivalent to the general Wiener-Hopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common el...
Let
be a real
-uniformly smooth Banach space with constant
Let
denote the class of functions
that are harmonic unival...
We reinvestigate the convergence properties of the SQP-type method for solving nonlinear semidefinite programming problems studied by Correa and Ramirez (2004). We prove, under the strong second-order sufficie...
The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most im...
and Applications
We use the
-binomial formula to establish two inequalities for the basic hypergeometric series
...
We use the potential theory to give integral representations of functions in the Sobolev spaces
, where
...
-Twisted Euler Polynomials and Numbers
The main purpose of this paper is to construct generating functions of higher-order twisted
-extension of Euler polynomials and numbers,...
This paper gives some local regularity results for minima of anisotropic functionals
...
We build a multiple Hilbert-type integral inequality with the symmetric kernel
and involving an integral operator
...
The extinction phenomenon of solutions for the homogeneous Dirichlet boundary value problem of the porous medium equation
, is studied. S...
This paper generalizes results of Cheung and Ma (2005) to more general inequalities with more than one distinct nonlinear term. From our results, some results of Cheung and Ma (2005) can be deduced as some spe...
In this paper, we reformulate and prove the Hyers-Ulam-Rassias stability theorem of the cubic functional equation
for fixed integer
We investigate properties of the zeros of solutions for higher-order periodic differential equations, and prove that under certain hypotheses, the convergence exponent of zeros of the product of two linearly i...
We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain a...
We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twis...
1-Order and Applications
Some character of the symmetric homogenous kernel of
1-order in Hilbert-type operator
...
We study the strong convergence of a hybrid steepest descent method with variable parameters for the general variational inequality (GVI)
Let
be a nonnegative Radon measure on
which satisfies the gr...
-Laplacian Equations with Singular Nonlinearities
This paper investigates the
-Laplacian equations with singular nonlinearities
Let
be a sequence of real numbers and let
be any
The purpose of the present paper is to introduce several new classes of analytic functions defined by using the Choi-Saigo-Srivastava operator associated with the Dziok-Srivastava operator and to investigate v...
We consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods. Our results in...
Integral means inequalities are obtained for the fractional derivatives of order
of functions belonging to a unified subclass of prestar...
We derive oscillation criteria for general-type neutral differential equations
...
We obtain an interesting subordination relation for Salagean-type certain analytic functions by using subordination theorem.
Some existence theorems of nonzero solutions and multiple solutions for a class of bilinear variational inequalities are studied in reflexive Banach spaces by fixed point index approach. The results presented ...
We establish generalizations of Steffensen's integral inequality on time scales via the diamond-
dynamic integral, which is defined as a...
-Laplacian Equations
We consider the oscillatory property of the following
-Laplacian equations
By virtue of an operator-theoretical approach, we deal with hyperbolic singular perturbation problems for integrodifferential equations. New convergence theorems for such singular perturbation problems are obt...
A new simple proof of Shafer-Fink-type inequality proposed by Malešević is given.
-Genocchi Numbers and Polynomials
We discuss new concept of the
-extension of Genocchi numbers and give some relations between
...
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