We consider the extremal problem of maximizing functions u in the class of real-valued biconvex functions satisfying a boundary condition ψ on a product of the unit ball with itself, with the ℓ p -norm. In 1986, Burkholder explicitly found the maximal function for p = 2 . In this paper, we find some characterizations of such extremal functions. We establish that sufficiently smooth ...

In this paper, we study the complete moment convergence of the sums of ρ̃-mixing sequences which are double-indexed randomly weighted and stochastically dominated by a random variable X. Under the different moment conditions on X and weights, many complete moment convergence and complete convergence results are obtained. Moreover, some simulations are given for illustration. MSC: ...

In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices. MSC: 15A60, 11B39, 15B05.

In this paper, we introduce the binomial sequence spaces b 0 r , s and b c r , s of nonabsolute type which include the spaces c 0 and c, respectively. Also, we prove that the spaces b 0 r , s and b c r , s are linearly isomorphic to the spaces c 0 and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their ...

In the article, we present the necessary and sufficient condition for the parameter p on the interval ( 7 / 5 , ∞ ) such that the function x → erf ( x ) / B p ( x ) is strictly increasing (decreasing) on ( 0 , ∞ ) , and find the best possible parameters p, q on the interval ( 7 / 5 , ∞ ) such that the double inequality B p ( x ) < erf ( x ) < B q ( x ) holds for all x > 0 , where ...

Let W = λ B + ν B H be a mixed-fractional Brownian motion with Hurst index 0 < H < 1 2 and λ , ν ≠ 0 . In this paper we study the quadratic covariation [ f ( W ) , W ] ( H ) defined by [ f ( W ) , W ] t ( H ) : = lim ε ↓ 0 1 ν 2 ε 2 H ∫ 0 t { f ( W s + ε ) − f ( W s ) } ( W s + ε − W s ) d η s in probability, where f is a Borel function and η s = λ 2 s + ν 2 s 2 H . For some ...

This paper is concerned with upper Hölder continuity and Hölder calmness of a perturbed vector optimization problem. We establish some new sufficient conditions for upper Hölder continuity and Hölder calmness of the perturbed solution mappings and the perturbed optimal value mappings of a vector optimization problem under the case that the objective function and the feasible set ...

Using Brouwer’s fixed point theorem, we prove the existence of solutions for some nonlinear problem with subcritical Sobolev exponent in S + 4 . MSC: 46E35, 47H10, 35J60.

In this work, we introduce the binomial sequence spaces b p r , s and b ∞ r , s which include the spaces ℓ p and ℓ ∞ , in turn. Moreover, we show that the spaces b p r , s and b ∞ r , s are BK-spaces and prove that these spaces are linearly isomorphic to the spaces ℓ p and ℓ ∞ , respectively. Furthermore, we speak of some inclusion relations and give the Schauder basis of the space ...

The authors first introduce the concepts of generalized ( α , m ) -preinvex function, generalized quasi m-preinvex function and explicitly ( α , m ) -preinvex function, and then provide some interesting properties for the newly introduced functions. The more important point is that we give a necessary and sufficient condition respecting the relationship between the generalized ( α ...

Let ( A 0 , A 1 ) be a compatible couple of normed spaces. We study the interrelation of the general K-interpolation spaces of the couple ( A 0 + A 1 , A 0 ∩ A 1 ) with those of the couples ( A 0 , A 1 ) , ( A 0 + A 1 , A 0 ) , ( A 0 + A 1 , A 1 ) , ( A 0 , A 0 ∩ A 1 ) , and ( A 1 , A 0 ∩ A 1 ) . MSC: 46B70.

We introduce a new concept of convexity that depends on a function F : R × R × R × ( 0 , 1 ) → R satisfying certain axioms. The presented concept generalizes many kinds of convexity including ε-convex functions, α-convex functions, and h-convex functions. Moreover, some integral inequalities are provided via our notion of convexity. MSC: 26A51, 26D15, 35A23.

In this paper, some complete convergence, complete moment convergence, and mean convergence results for arrays of rowwise asymptotically negatively associated (ANA) random variables are obtained. These theorems not only generalize some well-known ones to ANA cases, but they also improve them. MSC: 60F15, 60F25.

In this paper, we employ iteration on operator version of the famous Young inequality and obtain more arithmetic-geometric mean inequalities and the reverse versions for positive operators. Concretely, we obtain refined Young inequalities with the Kantorovich constant, the reverse ratio type and difference type inequalities for arithmetic-geometric operator mean under different ...

Recently, Sofonea (Gen. Math. 16:47-54, 2008 ) considered some relations in the context of quantum calculus associated with the q-derivative operator D q and divided difference. As applications of the post-quantum calculus known as the ( p , q ) -calculus, we derive several relations involving the ( p , q ) -derivative operator and divided differences. MSC: 11B68, 11B83, 81S40.

The main purpose of this paper is to establish a boundedness result for strong maximal functions with respect to certain non-doubling measures in R n . More precisely, let d μ ( x 1 , … , x n ) = d μ 1 ( x 1 ) ⋯ d μ n ( x n ) be a product measure which is not necessarily doubling in R n (only assuming d μ i is doubling on R for i = 2 , … , n ), and let ω be a nonnegative and ...

Let q ≥ 2 be a fixed integer, A = A ( q ) ≤ q , B = B ( q ) ≤ q , and H = H ( q ) ≤ q . Define ħ ( A , B , H ) = { a ∈ Z ∣ ( a , q ) = 1 , a b ≡ 1 ( mod q ) , 1 ≤ a ≤ A , 1 ≤ b ≤ B , | a − b | ≤ H } . With the aid of the estimates for the general Kloosterman sums and the properties of trigonometric sums, we obtain an upper bound of the general partial Gaussian sums over the number ...

It is well known that the second-order cone and the circular cone have many analogous properties. In particular, there exists an important distance inequality associated with the second-order cone and the circular cone. The inequality indicates that the distances of arbitrary points to the second-order cone and the circular cone are equivalent, which is crucial in analyzing the ...

We study a very particular anticipated BSDEs when the driver is time-changing Lévy noise. We give an estimate of the solutions in the system satisfying some non-Lipschitz conditions. Also, we state an useful comparison theorem for the solutions. At last, we establish another specific Feynman-Kac formula for a quasilinear PDE.

In this paper, we present a direct method to solve the least-squares Hermitian problem of the complex matrix equation ( A X B , C X D ) = ( E , F ) with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, F. This method determines the least-squares Hermitian solution with the minimum norm. It relies on a matrix-vector product and the Moore-Penrose ...

In this paper, we establish some boundedness conditions for the multidimensional Hausdorff operator on the homogeneous Hardy-Morrey and on the Besov-Morrey space, and we extend some results in the recent papers by Jia and Wang, and by Mazzucato, respectively. The main tool we implement in the study is the decomposition of the given function spaces in terms of atoms (smooth atoms ...

This paper deals with an unstirred chemostat model with the Beddington-DeAngelis functional response. First, some prior estimates for positive solutions are proved by the maximum principle and the method of upper and lower solutions. Second, the calculation on the fixed point index of chemostat model is obtained by degree theory and the homotopy invariance theorem. Finally, some ...

We present in this paper a necessary and sufficient condition to establish the inequality between generalized weighted means which share the same sequence of numbers but differ in the weights. We first present a sufficient condition, and then obtain the more general, necessary and sufficient, condition. Our results were motivated by an inequality, involving harmonic means, found in ...

In this article, we investigate the bounded perturbation resilience of the viscosity algorithm and propose the superiorized version of the viscosity algorithm. The convergence of the proposed algorithm is analyzed for a nonexpansive mapping. A modified viscosity algorithm and its convergence is presented.

In this paper, we establish the Newton-Kantorovich convergence theorem of a fourth-order super-Halley method under weaker conditions in Banach space, which is used to solve the nonlinear equations. Finally, some examples are provided to show the application of our theorem. MSC: 65J15, 65H10, 65G99, 47J25, 49M15.