Abstract: We study a singularly perturbed PDE with quadratic nonlinearity depending on a complex perturbation parameter . The problem involves an irregular singularity in time, as in a recent work of the author and A. Lastra, but possesses also, as a new feature, a turning point at the origin in . We construct a family of sectorial meromorphic solutions obtained as a small perturbation in of a slow curve of the equation in some time scale. We show that the nonsingular parts of these solutions share common formal power series (that generally diverge) in as Gevrey asymptotic expansion of some order depending on data arising both from the turning point and from the irregular singular point of the main problem. PubDate: Wed, 13 Sep 2017 00:00:00 +000

Abstract: Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be maximal monotone, be bounded and of type and be compact with such that lies in (i.e., there exist and such that for all ). A new topological degree theory is developed for operators of the type . The theory is essential because no degree theory and/or existence result is available to address solvability of operator inclusions involving operators of the type , where is not defined everywhere. Consequently, new existence theorems are provided. The existence theorem due to Asfaw and Kartsatos is improved. The theory is applied to prove existence of weak solution (s) for a nonlinear parabolic problem in appropriate Sobolev spaces. PubDate: Tue, 12 Sep 2017 09:06:02 +000

Abstract: We investigate global dynamics of the following systems of difference equations , , , where the parameters , , , , , and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space. PubDate: Wed, 02 Aug 2017 06:27:23 +000

Abstract: The purpose of this paper is to establish a weighted Montgomery identity for points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for points. For we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction. PubDate: Sun, 30 Jul 2017 07:57:07 +000

Abstract: We introduce the Szász and Chlodowsky operators based on Gould-Hopper polynomials and study the statistical convergence of these operators in a weighted space of functions on a positive semiaxis. Further, a Voronovskaja type result is obtained for the operators containing Gould-Hopper polynomials. Finally, some graphical examples for the convergence of this type of operator are given. PubDate: Wed, 26 Jul 2017 00:00:00 +000

Abstract: We establish some generalized Hölder’s and Minkowski’s inequalities for Jackson’s -integral. As applications, we derive some inequalities involving the incomplete -Gamma function. PubDate: Sun, 16 Jul 2017 08:30:14 +000

Abstract: We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions. PubDate: Sun, 11 Jun 2017 00:00:00 +000

Abstract: A novel class of --contraction for a pair of mappings is introduced in the setting of -metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. PubDate: Sun, 11 Jun 2017 00:00:00 +000

Abstract: Motivated by a number of recent investigations, we consider a new analogue of Bernstein-Durrmeyer operators based on certain variants. We derive some approximation properties of these operators. We also compute local approximation and Voronovskaja type asymptotic formula. We illustrate the convergence of aforementioned operators by making use of the software MATLAB which we stated in the paper. PubDate: Tue, 30 May 2017 00:00:00 +000

Abstract: We consider a nonautonomous 2D Leray- model of fluid turbulence. We prove the existence of the uniform attractor . We also study the convergence of as goes to zero. More precisely, we prove that the uniform attractor converges to the uniform attractor of the 2D Navier-Stokes system as tends to zero. PubDate: Wed, 17 May 2017 00:00:00 +000

Abstract: We give a necessary and sufficient condition for the boundedness of the Bergman fractional operators. PubDate: Wed, 10 May 2017 00:00:00 +000

Abstract: This paper deals with matrix transformations that preserve the -convexity of sequences. The main result gives the necessary and sufficient conditions for a nonnegative infinite matrix to preserve the -convexity of sequences. Further, we give examples of such matrices for different values of and . PubDate: Tue, 02 May 2017 08:18:23 +000

Abstract: We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (-time scale). PubDate: Tue, 18 Apr 2017 00:00:00 +000

Abstract: We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration. PubDate: Mon, 10 Apr 2017 00:00:00 +000

Abstract: In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities. PubDate: Tue, 21 Mar 2017 07:02:36 +000

Abstract: In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem. PubDate: Tue, 21 Mar 2017 06:19:03 +000

Abstract: Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional methods. PubDate: Sun, 05 Mar 2017 10:20:04 +000

Abstract: We consider two families of multilinear Hilbert-type operators for which we give exact relations between the parameters so that they are bounded. We also find the exact norm of these operators. PubDate: Wed, 08 Feb 2017 09:02:13 +000

Abstract: The continuous quaternion wavelet transform (CQWT) is a generalization of the classical continuous wavelet transform within the context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to establish logarithmic uncertainty principles related to generalized transform. PubDate: Mon, 30 Jan 2017 00:00:00 +000