In this paper, we introduce some new concepts to the field of probability theory: \(\left( k,s\right) \)-Riemann–Liouville fractional expectation and variance functions. Some generalized integral inequalities are established for \(\left( k,s\right) \)-Riemann–Liouville expectation and variance functions.

We study the nonexistence of nontrivial solutions for the nonlinear elliptic system $$\begin{aligned} \left\{ \begin{array}{lll} (-\Delta _x)^{\alpha /2}u+|x|^{2\delta } (-\Delta _y)^{\beta /2}u+|x|^{2\eta }|y|^{2\theta } (-\Delta _z)^{\gamma /2}u&{}=&{} v^p,\\ \\ (-\Delta _x)^{\mu /2}v+|x|^{2\delta } (-\Delta _y)^{\nu /2}v+|x|^{2\eta }|y|^{2\theta } (-\Delta _z)^{\sigma /2}v...

Let a simply-connected homogeneous space \({X}\) satisfy the condition of \({{\rm dim} \pi_{\rm even}(X)\otimes {\mathbb{Q}}=2}\) and \({{\rm dim} \pi_{\rm odd}(X)\otimes {\mathbb{Q}}=3}\) (then, we say it is of (2, 3) type), which is the smallest rank in non-formal pure spaces. Then, we compute the Sullivan minimal model of the Dold–Lashof classifying space \({{\rm Baut}_1 X...

In this paper, we consider the problem of prescribing scalar curvature under minimal boundary conditions on the standard four-dimensional half sphere. We describe the lack of compactness of the associated variational problem and we give new existence and multiplicity results.

Let M be a module over a commutative ring R. The annihilating-submodule graph of M, denoted by AG(M), is a simple graph in which a non-zero submodule N of M is a vertex if and only if there exists a non-zero proper submodule K of M such that N K = (0), where N K, the product of N and K, is denoted by (N : M)(K : M)M and two distinct vertices N and K are adjacent if and only if N...

In this paper, we introduce a cyclic subgradient extragradient algorithm and its modified form for finding a solution of a system of equilibrium problems for a class of pseudomonotone and Lipschitz-type continuous bifunctions. The main idea of these algorithms originates from several previously known results for variational inequalities. The proposed algorithms are extensions of...

In this paper, we introduce (p, q)-Bernstein Durrmeyer operators. We define (p, q)-beta integral and use it to obtain the moments of the operators. We obtain uniform convergence of the operators by using Korovkin’s theorem. We estimate direct results of the operators by means of modulus of continuity and Peetre K-functional. Finally, we find Voronovskaya-type theorem for the...

We prove some new theta-function identities for two continued fractions of Ramanujan which are analogous to those of Ramanujan–Göllnitz–Gordon continued fraction. Then these identities are used to prove new general theorems for the explicit evaluations of the continued fractions.

A class of periodic boundary value problems for higher order fractional differential equations with impulse effects is considered. We first convert the problem to an equivalent integral equation. Then, using a fixed-point theorem in Banach space, we establish existence results of solutions for this kind of boundary value problem for impulsive singular higher order fractional...

Let A be a \({\mathbb{k}}\)-algebra and \({A[t; \alpha,\delta]}\) its Ore extension. We give a pair of adjoint functors between the module category over ker \(\delta\) and the module category over \({A[t; \alpha,\delta]}\). For a kind of special Ore extensions, this pair describes an equivalence between the module category over ker \({\delta}\) and an appropriate subcategory of...

We investigate problems of estimating the deviation of functions from their de la Vallée-Poussin sums in weighted Orlicz spaces L M (T, ω) in terms of the best approximation \({E_{n}(f)_{M, \, \omega }}\).

In this article, a numerical technique is developed for solving delay differential equations. The proposed method combines the method of steps with the radial basis function networks. A delay differential equation is transformed to an ordinary differential equation and then the radial basis function collocationmethod is implemented to find the solution of the ordinary...

In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called quasi generalized Cauchy–Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficient conditions for some distributions to be integrable.

The goal of this paper is to give useful method for solving a problem in biologic system that is formulated by stochastic Volterra integral equations. Here, we consider triangular functions, block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the validity and applicability of the operational matrices.

Here, we have estimated the order of magnitude of multiple Walsh–Fourier coefficients of functions of \({\phi(\Lambda^1,\ldots,\Lambda^N)BV([0,1]^{N})}\).

Recently, Krasner (m, n)-hyperrings were introduced and analyzed by Davvaz et. al. This is a suitable generalization of Krasner hyperrings. In this research work, we consider that if I is a normal hyperideal of a Krasner (m, n)-hyperring R, then the quotient hyperring [R : I*] is an (m, n)-ring. Moreover, we prove that if R is a multiplicative (m, n)-ary hyperring and I is a...

This paper deals with some existence and Ulam stability results for a class of partial integral equations via Hadamard’s fractional integral, by applying Schauder’s fixed-point theorem.

For a positive integer k ≥ 2, the kth-order slant weighted Toeplitz operator \({U_{k,\phi}^{\beta}}\) on \({L^{2}(\beta)}\) with \({\phi \in L^{\infty}(\beta)}\) is defined as \({U_{k,\phi}^{\beta}=W_{k}M_{\phi}^{\beta}}\), where \({W_{k}e_{n}(z)=\frac{\beta_{m}}{\beta_{km}}e_m(z)}\) if \({n=km, m\in\mathbb{Z}}\) and \({W_{k}e_n(z)= 0}\) if n ≠ km. The paper derives relations...

In this paper, we establish sufficient conditions for the existence of local solutions for a class of Cauchy type problems with arbitrary fractional order. The results are established by the application of the contraction mapping principle and Schaefer’s fixed point theorem. An example is provided to illustrate the applicability of the results.

A numerical scheme combining the features of quintic Hermite interpolating polynomials and orthogonal collocation method has been presented to solve the well-known non-linear Burgers’ equation. The quintic Hermite collocation method (QHCM) solves the non-linear Burgers’ equation directly without converting it into linear form using Hopf–Cole transformation. Stability of the QHCM...

The non-linear blood flow under the influence of periodic body acceleration through a generalized multiple stenosed artery is investigated with the help of numerical simulation. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier–Stokes equation. The non-linear equation is solved numerically using...

The K λ-means were first introduced by Karamata. Vučković first studied the K λ-summability of a Fourier series and later on Lal studied the K λ-summability of a conjugate series. In the present paper, we have studied the |K λ|-summability of Fourier series and conjugate series.

This work is concerned with the existence of at least three nonzero solutions for a boundary value problem posed on the half-line. The method we employ is based upon Morse theory and uses \({H^1_{0,p}}\) versus \({C^1_{p}}\) local minimizers.

In this paper, we study Shannon’s entropy and Fisher information number for concomitants of generalized order statistics from subfamilies of Farlie–Gumbel–Morgenstern when the marginal distributions are Weibull, exponential, Pareto and power function. Also, we provide some numerical results of Shannon entropy and Fisher information number for concomitants of order statistics.