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Pontryagin’s maximum principle for an optimal control system governed by an ordinary differential equation with endpoint constraints is proved under the assumption that the control domain has no linear structu...
In this paper, we suggest and analyze an iterative method for solving the equilibrium problems on Hadamard manifolds using the auxiliary principle technique. We also consider the convergence analysis of the pr...
In this paper, we establish the complete convergence and complete moment convergence and obtain the equivalence of the complete convergence and complete moment convergence for the class of random variables sat...
As an alternative to classical calculus, Grossman and Katz (Non-Newtonian Calculus, 1972) introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus etc. ...
The purpose of this paper is to investigate some interesting identities on the Bernoulli and Euler polynomials arising from the orthogonality of Legendre polynomials in the inner product space
We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by the improvements of Young’s inequality. We also give a generalized Han’s inequality.
In this paper, we introduce the concepts of lacunary statistical τ-convergence, lacunary statistically τ-bounded and lacunary statistically τ-Cauchy in the framework of locally solid Riesz spaces. We also define ...
Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of st...
In this note, we derive, under some natural assumptions, a general pattern of the almost sure central limit theorem in the joint version for the maxima and sums.
Two problems are discussed in this paper. In the first problem, we consider one homogeneous and one non-homogeneous differential equations and study when the solutions of these differential equations can have ...
We will show certain functional inequalities involving fractional powers, making use of the Furuta inequality and Tanahashi’s argument.
We consider boundary regularity for weak solutions of quasilinear elliptic systems with the supquadratic growth condition and obtain a general criterion for a weak solution to be regular in the neighborhood of...
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...
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