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We investigate the Hyers-Ulam stability of the quadratic functional equation on restricted domains. Applying these results, we study of an asymptotic behavior of these quadratic mappings.
-Normed Spaces
We achieve the general solution of the quintic functional equation
and the sextic functional equation
...
On the hypothesis that the
th moments of the Hardy
-function...
We show that the function
is strictly logarithmically completely monotonic on
...
Some nonlinear weakly singular integral inequalities in two variables which generalize some known results are discussed. The results can be used as powerful tools in the analysis of certain classes of differen...
We introduce a generalized quadratic functional equation
, where
We determine the condition on
,
,
...
A new delay integral inequality is established. Using this inequality and the properties of nonnegative matrix, the attracting sets for the nonlinear functional differential equations with distributed delays a...
We introduce the vector-valued sequence spaces
,
, and
-Laplacian Impulsive Integrodifferential System with Multipoint and Integral Boundary Value Conditions
By the Leray-Schauder's degree, the existence of solutions for a weighted
-Laplacian impulsive integro-differential system with multi-point and ...
We establish some new Fejér-type inequalities for convex functions.
-adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials
The purpose of this paper is to give some properties of several Bernstein type polynomials to represent the fermionic
-adic integral on
Let
be a simple graph with
vertices, and let
Analyzing voting on income taxation usually implies mathematically cumbersome models. Moreover, a majority voting winner does not usually exist in such setups. Therefore, it is important to mathematically desc...
Here, we study the continuity of integral operators with operator-valued kernels. Particularly we get
estimates under some natural cond...
and Regularity Condition
We give a new proof for power-type weighted Hardy inequality in the norms of generalized Lebesgue spaces
. Assuming the logarithmic cond...
We give some refinements of the inequalities of Aczél, Popoviciu, and Bellman. Also, we give some results related to power sums.
Two-weighted norm estimates with general weights for Hardy-type transforms and potentials in variable exponent Lebesgue spaces defined on quasimetric measure spaces
...
Global phase synchronization for a class of dynamical complex networks composed of multiinput multioutput pendulum-like systems with time-varying coupling delays is investigated. The problem of the global phas...
For
, the generalized logarithmic mean
, arithmetic mean
We investigate an impulsive predator-prey system with Monod-Haldane type functional response and control strategies, especially, biological and chemical controls. Conditions for the stability of the prey-free ...
We give the best lower bound for the weighted Jensen's discrete inequality with ordered variables applied to a convex function
, in the ...
For
, the power-type Heron mean
and the Seiffert mean
We study a class of stochastic bi-criteria optimization problems with one quadratic and one linear objective functions and some linear inequality constraints. A hybrid method of chance-constrained programming ...
We introduce and study the general nonlinear random
-accretive equations with random fuzzy mappings. By using the resolvent technique fo...
Two open problems were posed in the work of Long and Chu (2010). In this paper, we give the solutions of these problems.
A new Hilbert-type linear operator with a composite kernel function is built. As the applications, two new more accurate operator inequalities and their equivalent forms are deduced. The constant factors in th...
We establish a generalization of the inequality introduced by Mitrinović and Pečarić in 1988. We prove mean value theorems of Cauchy type for that new inequality by taking its difference. Furthermore, we prove...
We introduce a new iterative scheme for finding a common element of the set of solutions of the equilibrium problems, the set of solutions of variational inequality for a relaxed cocoercive mapping, and the se...
A Hájek-Rényi-type maximal inequality is established for multidimensional arrays of random elements. Using this result, we establish some strong laws of large numbers for multidimensional arrays. We also provi...
We introduce the system of variational inequality problems for semimonotone operators in reflexive Banach space. Using the Kakutani-Fan-Glicksberg fixed point theorem, we obtain some existence results for syst...
We prove some results for convex combination of nonnegative functionals, and some corollaries are established.
By applying the way of weight functions and a Hardy's integral inequality, a Hilbert-Hardy-type integral operator is defined, and the norm of operator is obtained. As applications, a new Hilbert-Hardy-type ine...
We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone,
-Mixing Random Variables and Its Applications
We give out a general method to prove the complete convergence for arrays of rowwise
-mixing random variables and to present some result...
We formulate and prove a converse for a generalization of the classical Minkowski's inequality. The case when
is also considered. Apply...
We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and deriv...
By using Doob's martingale convergence theorem, this paper presents a class of strong limit theorems for arbitrary stochastic sequence. Chow's two strong limit theorems for martingale-difference sequence and L...
Two adjacent recursive processes converging to the mean value of a real-valued convex function are given. Refinements of the Hermite-Hadamard inequality are obtained. Some applications to the special means are...
We will investigate the superstability of the sine functional equation from the following Pexider-type functional equation
(
We study some nonlinear dynamic integral inequalities on time scales by introducing two adjusting parameters, which provide improved bounds on unknown functions. Our results include many existing ones in the l...
We generalize means of Stolarsky type and show the monotonicity of these generalized means.
Some improvements of classical Jensen's inequality are used to define the weighted mixed symmetric means. Exponential convexity and mean value theorems are proved for the differences of these improved inequali...
A new class of generalized V-type I invex functions is introduced for nonsmooth multiobjective programming problem. Based upon these generalized invex functions, we establish sufficient optimality conditions f...
We suggest new dual algorithms and iterative methods for solving monotone generalized variational inequalities. Instead of working on the primal space, this method performs a dual step on the dual space by usi...
-Adic
-Integral on
Associated with Twisted
-Bernoulli Polynomials and Numbers
Recently, many authors have studied twisted
-Bernoulli polynomials by using the
...
-Bernoulli Numbers and Polynomials Associated with
-Volkenborn Integrals
We give some interesting equation of
-adic
-integrals on
-Euler Numbers Associated with the Fermionic
-Adic Integral on
We consider the following problem in the paper of Kim et al. (2010): "Find Witt's formula for Carlitz's type
-Euler numbers." We give Wi...
We consider some new nonlinear retarded integral inequalities with two variables, which extend the results in the work of W.-S. Wang (2007), and the one in the work of Y.-H. kim (2009). These inequalities incl...
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