Journal of Mathematical Extension
Volume:15 Issue: 4, Autumn 2021

We introduce the idea of S JS-metric spaces which is a generalization of S-metric spaces. Next we study the properties of S JS-metric spaces and prove several theorems. We also deal with abstract S JS - topological spaces induced by S JS-metric and obtain several classical results including Cantor’s intersection theorem in this setting.

It is well known that bias in parameter estimates arises when there are measurement errors in the covariates of regression models. One solution for decreasing such biases is the use of prior information concerning the measurement error, which is often called replication data. In this paper, we present a ridge estimator in replicated measurement error (RMER) to overcome the multicollinearity problem in such models. The performance of RMER against some other estimators is investigated. Large sample properties of our estimator are derived and compared with other estimators using a simulation study as well as a real data set.

In this paper we will introduce the integral closure of a filtration relative to an injective module

In this article, an outer measure is constructed on a pseudoordered set (X, ≿) and then it will be shown that it is in fact a measure defined on the whole power set of X . Applying this, a measurable utility function θ is defined which represents the relation ≿ on X. Also, we discuss the continuity and upper semi-continuity of θ in certain points of X. Finally, the results are used to improve some of the theorems in economics.

.Consider the triple (M, g, dµ) as a smooth metric measure space and M is an n-dimensional compact Riemannian manifold without boundary, also dµ = e −f(x) dV is a weighted measure. We are going to investigate the evolution problem for the first eigenvalue of the weighted (p, q)-Laplacian system along the rescaled Yamabe flow and we hope find some monotonic quantities.

In this paper, we introduce a hemi-slant submanifold of a 3-Sasakian manifold. First, we obtain some new results in terms of the operators Ti and fi. By using Gauss, Codazzi and Ricci equations, we prove some results involving Ricci and scalar curvatures by using the slant angle and the mean curvature vector of the submanifold.

In this note, we study Cauchy-Schwarz-type inequality for fractional Strum-Liouville boundary value problem containing Caputo derivative of order α, 1 < α ≤ 2. A lower bound for the smallest eigenvalue is determined using this inequality. We give a comparison between the smallest eigenvalue and its lower bound obtained from the Lyapunov-type and Cauchy-Schwarz-type inequalities which indicate the properties of eigenvalues.

The purpose of this paper is to define a new class of analytic, normalized functions in the open unit disk D = {z : z ∈ C and |z| < 1} subordinating with crescent shaped regions, and to derive certain coefficient estimates a2 , a3 and Fekete-Szeg¨o inequality for f ∈ Mq(α, β, λ). A similar result have been done for the function f −1 . Further application of our results to certain functions defined by convolution products with a normalized analytic function is given, in particular we obtain FeketeSzeg¨o inequalities for certai

In this paper, we conjecture that the symmetric diagonal Diophantine equation x 6 + ky3 + k 0 z 3 = u 6 + kv3 + k 0w 3 has infinitely many nontrivial solutions for all rational numbers k and k 0 . This conjecture is proved for certain cases.

In this paper, we present a general version of operator Bellman inequality. Also, the refinement of inequality due to J. Aujla and F. Silva for the convex functions is given as well.

The aim of this paper is to introduce an efficient meshless element free Galerkin technique for solving elliptic interface problems. In this work, the second-order elliptic equation with discontinuous coefficients and homogeneous and nonhomogeneous jump conditions is considered. Moving kriging interpolation is chosen to construct shape functions in the proposed method. To apply the jump conditions in the weak form of the problem, Nitsche’s method is used. Some examples are presented to confirm the effectiveness of the proposed method for interface problems.

The aim of this paper is to study unitary regular modules on commutative rings with identity. Regularity accompanied by cocyclic property results in some prime-related conclusions on both modules and rings. Further to this, regularity addresses also radical property of submodules and they are related closely. This property not only affects the modules on ring R but also restricts R to totally idempotent one.

In this paper, we introduce a new method for solving fuzzy Bernoulli differential equation (FBDE) under generalized differentiability. At the beginning, by stating the theorems, we define n th power of LR fuzzy function and the derivative of LR fuzzy function. Then, we obtain core function to determine LR fuzzy solution, through solving 1-cut FBDE, and calculate spread functions by finding the sign of real valued functions of coefficients of FBDE and finding the sign of core function. Also, numerical examples are presented to verify the effectiveness of the proposed method.

Solving optimal control problems (OCP) with analytical methods has usually been difficult or not cost-effective. Therefore, solving these problems requires numerical methods. There are, of course, many ways to solve these problems. One of the methods available to solve OCP is a forward-backward sweep method (FBSM). In this method, the state variable is solved in a forward and co-state variable by a backward method where an explicit Runge–Kutta method (ERK) is often used to solve differential equations arising from OCP. In this paper, instead of the ERK method, three hybrid methods based on ERK method of order 3 and 4 are proposed for the numerical approximation of the OCP. Truncation errors and stability analysis of the presented methods are illustrated. Finally, numerical results of the four optimal control problems obtained by new methods, which shows that new methods give us more detailed results, are compared with those of ERK approaches of orders 3 and 4 for solving OCP.

In 1964, Levinson [4] proved integral inequalities concerning generalization of Hardy’s inequalities. In this paper two results are given. First one is extension of the Levinson Integral inequalities via convexity and the second is for the Levinson Integral inequalities of Hardy, this inequalities are established for p < 1 and some related inequalities are also considered with a sharp constant.

In this paper, multiobjective optimization problems with nondifferentiable quasiconvex functions are considered. We obtain some duality results and a linear representation for the considered problems. Since the well-known strong duality result is not valid for the problems, we present a weaker form of it, named quasi-strong duality result.

In this paper, for any two elements y, u of a BCK-algebra X, we assign a subset of X, denoted by Sy(u), and investigate some related properties. We show that Sy(u) is a subalgebra of X for all y, u ∈ X. Using these subalgebras, we characterize the involutive BCK-algebras, and give a necessary and sufficient condition for a bounded BCK-algebra to be a commutative BCK-chain. Finally, we show that the set of all subalgebras Sy(u) forms a bounded distributive lattice.

Isoparametric hypersurfaces of Lorentz-Minkowski spaces, which has been classified by M.A. Magid in 1985, have motivated some researchers to study biconservative hypersurfaces. A biconservative hypersurface has conservative stress-energy with respect to the bienergy functional. A timelike (Lorentzian) hypersurface x : Mn 1 → E n+1 1 , isometrically immersed into the Lorentz-Minkowski space E n+1 1 , is said to be biconservative if the tangent component of vector field ∆2x on Mn 1 is identically zero. In this paper, we study the Lk-extension of biconservativity condition. The map Lk on a hypersurface (as the kth extension of Laplace operator L0 = ∆) is the linearized operator arisen from the first variation of (k + 1)th mean curvature of hypersurface. After illustrating some examples, we prove that an Lk-biconservative timlike hypersurface of E n+1 1 , with at most two distinct principal curvatures and some additional conditions, is isoparametric.