Georgian Mathematical Journal
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Published By Walter De Gruyter Gmbh

1572-9176, 1072-947x

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
İlker Gençtürk ◽  
Yankis R. Linares

Abstract In this paper, we study a Robin condition for the inhomogeneous Cauchy–Riemann equation w z ¯ = f {w_{\bar{z}}=f} in a ring domain R, by reformulating it as a Dirichlet boundary condition.


2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Petre Babilua ◽  
Elizbar Nadaraya

Abstract In the paper, the limiting distribution is established for an integral square deviation of estimates of Bernoulli regression functions based on two group samples. Based on these results, the new test is constructed for the hypothesis testing on the equality of two Bernoulli regression functions. The question of consistency of the constructed test is studied, and the asymptotic of the test power is investigated for some close alternatives.


2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Petre Babilua

Abstract The estimate for the Bernoulli regression function is constructed using the Bernstein polynomial for group observations. The question of its consistency and asymptotic normality is studied. A testing hypothesis is constructed on the form of the Bernoulli regression function. The consistency of the constructed tests is investigated.


2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Vakhtang Tsagareishvili

Abstract In the paper we consider the properties of Fourier coefficients of functions that possess derivatives of bounded variation. We investigate the convergence of the special series of Fourier coefficients with respect to general orthonormal systems (ONS). The obtained results are the best possible. We also describe the behavior of subsequences of general ONS.


2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Fatima Bahidi ◽  
Bilel Krichen ◽  
Bilel Mefteh

Abstract The purpose of this paper is to prove some fixed point results dealing with a system of nonlinear equations defined in an angelic Hausdorff locally convex space ( X , { | ⋅ | p } p ∈ Λ ) (X,\{\lvert\,{\cdot}\,\rvert_{p}\}_{p\in\Lambda}) having the 𝜏-Krein–Šmulian property, where 𝜏 is a weaker Hausdorff locally convex topology of 𝑋. The method applied in our study is connected with a family Φ Λ τ \Phi_{\Lambda}^{\tau} -MNC of measures of weak noncompactness and with the concept of 𝜏-sequential continuity. As a special case, we discuss the existence of solutions for a 2 × 2 2\times 2 block operator matrix with nonlinear inputs. Furthermore, we give an illustrative example for a system of nonlinear integral equations in the space C ⁢ ( R + ) × C ⁢ ( R + ) C(\mathbb{R}^{+})\times C(\mathbb{R}^{+}) to verify the effectiveness and applicability of our main result.


2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Musa Cakir ◽  
Baransel Gunes

Abstract In this study, singularly perturbed mixed integro-differential equations (SPMIDEs) are taken into account. First, the asymptotic behavior of the solution is investigated. Then, by using interpolating quadrature rules and an exponential basis function, the finite difference scheme is constructed on a uniform mesh. The stability and convergence of the proposed scheme are analyzed in the discrete maximum norm. Some numerical examples are solved, and numerical outcomes are obtained.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nugzar Shavlakadze ◽  
Otar Jokhadze

Abstract Exact and approximate solutions of a some type singular integro-differential equation related to problems of adhesive interaction between elastic thin half-infinite or finite homogeneous patch and elastic plate are investigated. For the patch loaded with vertical forces, there holds a standard model in which vertical elastic displacements are assumed to be constant. Using the theory of analytic functions, integral transforms and orthogonal polynomials, the singular integro-differential equation is reduced to a different boundary value problem of the theory of analytic functions or to an infinite system of linear algebraic equations. Exact or approximate solutions of such problems and asymptotic estimates of normal contact stresses are obtained.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Bahrom Y. Irgashev

Abstract In the paper, similarity solutions are constructed for a model equation with multiple characteristics of an arbitrary integer order. It is shown that the structure of similarity solutions depends on the mutual simplicity of the orders of derivatives with respect to the variable x and y, respectively. Frequent cases are considered in which they are shown as fundamental solutions of well-known equations, expressed in a linear way through the constructed similarity solutions.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Agil K. Khanmamedov ◽  
Khatira E. Abbasova

Abstract In the present paper, it is indicated that the proof of the main lemma is not valid, which relates to the inverse scattering problem for the perturbed Stark operator on the semiaxis. A correct proof of the mentioned lemma is given.


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