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We will show certain functional inequalities involving fractional powers, making use of the Furuta inequality and Tanahashi’s argument.
In the present paper, we will give some new notions, such as Δ-convergence and Δ-Cauchy, by using the Δ-density and investigate their relations. It is important to say that the results presented in this work g...
The existence of a positive solution of a p-Laplace-like equation with critical growth is established by the generalization to the concentration-compactness principle and the Sobolev inequality under some proper ...
In this paper, we prove general fixed point theorems for self-maps of a partially ordered complete metric space which satisfy an implicit type relation. Our method relies on constructive arguments involving Pi...
In this paper, some inequalities for a linearly negative quadrant dependent (LNQD) sequence are obtained. As their application, the asymptotic normality of the weight function estimate for a regression functio...
For a system of nonlinear inequalities, we approximate it by a family of parameterized smooth equations via a new smoothing function. We present a new smoothing and regularization predictor-corrector algorithm...
The study of operators plays a vital role in mathematics. To define an operator using the convolution theory, and then study its properties, is one of the hot areas of current ongoing research in the geometric...
In this paper, in order to make the convergence faster to a function being approximated, we introduce a kind of complex modified q-Durrmeyer type operators which can reproduce constant and linear functions. We st...
Recently, the concept of statistical convergence has been studied in 2-normed and random 2-normed spaces by various authors. In this paper, we shall introduce the concept of λ-double statistical convergence and λ
The Blasius problem has been used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past a flat plate moving at a constant speed β; and it is well known that there exists the ...
This paper deals with the construction of anisotropic curl-free wavelets that satisfy the tangent boundary conditions on bounded domains. Based on some assumptions, we first obtain the desired curl-free Riesz ...
In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed additive and quadratic functional equation:
...
In this paper, we give a reversed version of a generalized Aczél’s inequality which is due to Wu and Debnath. As an application, an integral type of the reversed version of the Aczél-Vasić-Pečarić inequality i...
In this paper, some new Gronwall-Bellman-type nonlinear dynamic inequalities containing integration on infinite intervals on time scales are established, which provides new bounds on unknown functions and can ...
In this manuscript, we extend, generalize and enrich some recent coupled fixed point theorems in the framework of partially ordered G-metric spaces in a way that is essentially more natural.
In this paper, the notion of weakly Ky Fan’s points of set-valued mappings is established, and we prove some existence theorems of weakly Ky Fan’s points for functions with no continuity or space with no compa...
In this paper, a class of semistrictly G-preinvex functions introduced by Luo and Wu (J. Comput. Appl. Math. 222:372-380, 2008) is further considered. Some properties of semistrictly G-preinvex functions are obta...
By using the Leggett-Williams fixed-point theorem, a series of Sturm-Liouville type boundary value problems are studied. We impose sufficient conditions on f and get the existence of at least three positive solut...
In this paper we introduce the concept of Bochner pg-frames for Banach spaces. We characterize the Bochner pg-frames and specify the optimal bounds of a Bochner pg-frame. Then we define a Bochner qg-Riesz basis a...
Using the fixed point method, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality and of the Cauchy-Jensen additive functional inequality in random normed spaces.
We establish some stability results concerning the functional equation
The Hilbert transform along curves is defined by the principal value integral. The pointwise existence of the principal value Hilbert transform can be educed from the appropriate estimates for the correspondin...
In this paper, we will investigate function spaces, including a Sobolev space, a Besov space and a Triebel-Lizorkin space, on the Laguerre hypergroup.
This paper is devoted to studying the singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces, which contain many classical surfaces as model examples, on the product domains
In the present paper, we deal with the composition of carathéodory and homotopy operators for differential forms satisfying the A-harmonic equation in the bounded and convex domain. We obtain estimates for the co...
In this paper, we concentrate our study to derive appropriate duality theorems for two types of second-order dual models of a nondifferentiable minimax fractional programming problem involving second-order α-univ...
In this paper, the generalized Hyers-Ulam-Rassias stability problem of radical quadratic and radical quartic functional equations in quasi-β-Banach spaces and then the stability by using subadditive and subquadra...
In this paper, we define some generalized hyperbolic function classes. We also introduce natural metrics in the generalized hyperbolic
By introducing two pairs of conjugate exponents and using the improved Euler-Maclaurin summation formula, we estimate the weight functions and obtain a half-discrete Hilbert-type inequality with the non-monoto...
In (J. Inequal. Appl. 2011:Article ID 55, Section 4, 2011), Jang and Park proved the Hyers-Ulam stability of quadratic ∗-derivations on Banach ∗-algebras. One can easily show that all the quadratic ∗-derivations
In this paper, for a fourth-order differential equation, we will establish some lower bounds for the distance between zeros of a nontrivial solution and also lower bounds for the distance between zeros of a so...
In this paper, we prove that, for every vector quasi-equilibrium problem, there exists at least one essential component of the set of its solutions. As application, we show that, for every system of vector qua...
We propose a new algorithm for solving systems of nonlinear equations with convex constraints which combines elements of Newton, the proximal point, and the projection method. The convergence of the whole sequ...
There are a lot of refinements of the discrete Jensen’s inequality, and this problem has been studied by many authors. It is also a natural problem to give analogous results for the classical Jensen’s inequali...
We reformulate the following quadratic functional equation:
In this paper, we consider the twisted q-Bernoulli numbers and polynomials with weight α by using the bosonic q-integral on
. From the c...
This paper introduces and studies a class of generalized multivariate Bernstein operators defined on the simplex. By means of the modulus of continuity and so-called Ditzian-Totik’s modulus of function, the di...
Using the fixed point and direct methods, we prove the generalized Hyers-Ulam stability of the following additive-quadratic functional equation in non-Archimedean normed spaces
In this paper, a modified simple penalty function is proposed for a constrained nonlinear programming problem by augmenting the dimension of the program with a variable that controls the weight of the penalty ...
In this paper, we study pathwise estimation of the global positive solutions for the stochastic functional Kolmogorov-type systems with infinite delay. Under some conditions, the growth rate of the solutions f...
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