Abstract: A general Ostrowski’s type inequality for double integrals is given. We utilize function whose partial derivative of order four exists and is bounded. PubDate: Sun, 03 Mar 2019 13:30:03 +000

Abstract: Via the concentration compactness principle, delicate energy estimates, the strong maximum principle, and the Mountain Pass lemma, the existence of positive solutions for a nonlinear PDE with multi-singular inverse square potentials and critical Sobolev-Hardy exponent is proved. This result extends several recent results on the topic. PubDate: Sun, 03 Mar 2019 12:05:19 +000

Abstract: We study convergence of solutions of a space and time inhomogeneous fractional wave equation on the quarter-plane to the stationary regime described by solutions of the Helmholtz equation. PubDate: Wed, 06 Feb 2019 09:05:13 +000

Abstract: In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations. PubDate: Sun, 03 Feb 2019 00:00:00 +000

Abstract: In this paper, we derive explicit determinantal representation formulas of general, Hermitian, and skew-Hermitian solutions to the generalized Sylvester matrix equation involving -Hermicity over the quaternion skew field within the framework of the theory of noncommutative column-row determinants. PubDate: Sun, 06 Jan 2019 14:15:01 +000

Abstract: In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains. By employing the technique introduced by Benci and Cerami (1991), we obtain at least distinct positive solutions. PubDate: Thu, 03 Jan 2019 08:05:11 +000

Abstract: In this work, we define a new class of functions of the Bernoulli type using the Riemann-Liouville fractional integral operator and derive a generating function for these class generalized functions. Then, these functions are employed to derive formulas for certain Dirichlet series. PubDate: Wed, 12 Dec 2018 07:07:58 +000

Abstract: The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem. PubDate: Sun, 09 Dec 2018 10:19:16 +000

Abstract: In this paper, the notion of -contractions is introduced and a new fixed point theorem for such contractions is established. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: In the present article, we introduce the second Kummer function with matrix parameters and examine its asymptotic behaviour relying on the residue theorem. Further, we provide a closed form of a solution of a Weber matrix differential equation and give a representation using the second Kummer function. PubDate: Sun, 02 Dec 2018 00:00:00 +000

Abstract: We consider the Dirichlet initial boundary value problem , where the exponents ,, and are given functions. We assume that is a bounded function. The aim of this paper is to deal with some qualitative properties of the solutions. Firstly, we prove that if , then any weak solution will be extinct in finite time when the initial data is small enough. Otherwise, when , we get the positivity of solutions for large . In the second part, we investigate the property of propagation from the initial data. For this purpose, we give a precise estimation of the support of the solution under the conditions that and either or a.e. Finally, we give a uniform localization of the support of solutions for all , in the case where a.e. and . PubDate: Thu, 08 Nov 2018 06:14:34 +000

Abstract: In this paper, some new results are obtained for the even order neutral delay difference equation , where is an even integer, which ensure that all solutions of the studied equation are oscillatory. Our results extend, include, and correct some of the existing results. Examples are provided to illustrate the importance of the main results. PubDate: Thu, 08 Nov 2018 00:00:00 +000

Abstract: In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated -quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability. PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: In this paper, we are concerned with the solution of the third-order nonlinear differential equation , satisfying the boundary conditions ,, and , as , where and The problem arises in the study of the opposing mixed convection approximation in a porous medium. We prove the existence, nonexistence, and the sign of convex and convex-concave solutions of the problem above according to the mixed convection parameter and the temperature parameter . PubDate: Thu, 01 Nov 2018 00:00:00 +000

Abstract: We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive. PubDate: Thu, 04 Oct 2018 08:31:09 +000

Abstract: In this paper, we consider a general symmetric diffusion semigroup on a topological space with a positive -finite measure, given, for , by an integral kernel operator: . As one of the contributions of our paper, we define a diffusion distance whose specification follows naturally from imposing a reasonable Lipschitz condition on diffused versions of arbitrary bounded functions. We next show that the mild assumption we make, that balls of positive radius have positive measure, is equivalent to a similar, and an even milder looking, geometric demand. In the main part of the paper, we establish that local convergence of to is equivalent to local equicontinuity (in ) of the family . As a corollary of our main result, we show that, for , converges locally to , as converges to . In the Appendix, we show that for very general metrics on , not necessarily arising from diffusion, , as R. Coifman and W. Leeb have assumed a quantitative version of this convergence, uniformly in , in their recent work introducing a family of multiscale diffusion distances and establishing quantitative results about the equivalence of a bounded function being Lipschitz, and the rate of convergence of to , as . We do not make such an assumption in the present work. PubDate: Tue, 02 Oct 2018 09:26:47 +000

Abstract: In this paper we introduce the notion of proximal -normal structure of pair of -admissible sets in modular spaces. We prove some results of best proximity points in this setting without recourse to Zorn’s lemma. We provide some examples to support our conclusions. PubDate: Tue, 02 Oct 2018 00:00:00 +000

Abstract: We establish the existence of a strong convergent selection of a modified Mann-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points of a multivalued (or single-valued) strictly pseudocontractive-type mapping and the set of solutions of an equilibrium problem for a bifunction in a real Hilbert space . This work is a continuation of the study on the computability and applicability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of a sequence of closed convex subsets of from an arbitrary and a sequence of the metric projections of into . The obtained result is a partial resolution of the controversy over the computability of such algorithms in the contemporary literature. PubDate: Mon, 01 Oct 2018 00:00:00 +000

Abstract: We study systems with different diffusions (local and nonlocal), mixed boundary conditions, and reaction terms. We prove existence and uniqueness of the solutions and then analyze global existence vs blow up in finite time. For blowing up solutions, we find asymptotic bounds for the blow-up rate. PubDate: Mon, 01 Oct 2018 00:00:00 +000

Abstract: This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H0 whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics and verified that each of the numerators and denominators in the statistic test followed a distribution of . Since there was a symmetric and idempotent matrix S, it could be proved that . Matrix was positive semidefinite and contained weighting matrix which had different values in every location; therefore matrix was not idempotent. If and was not idempotent and also was a distributed random vector, then there were constants and ; hence ; therefore it was concluded that test statistic followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia. PubDate: Wed, 12 Sep 2018 07:39:55 +000

Abstract: Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number . PubDate: Tue, 14 Aug 2018 00:00:00 +000

Abstract: Let be a smoothly bounded pseudoconvex domain in and assume that where , the boundary of . Then we get optimal estimates of the Bergman kernel function along some “almost tangential curve” . PubDate: Wed, 18 Jul 2018 00:00:00 +000

Abstract: Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be a maximal monotone operator and be bounded and continuous with . The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the type provided that is compact or is of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition on . The operator is neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems. PubDate: Thu, 12 Jul 2018 09:04:35 +000

Abstract: We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration. PubDate: Mon, 02 Jul 2018 00:00:00 +000

Abstract: Through a modification on the parameters associated with generating function of the -extensions for the Apostol type polynomials of order and level , we obtain some new results related to a unified presentation of the -analog of the generalized Apostol type polynomials of order and level . In addition, we introduce some algebraic and differential properties for the -analog of the generalized Apostol type polynomials of order and level and the relation of these with the -Stirling numbers of the second kind, the generalized -Bernoulli polynomials of level , the generalized -Apostol type Bernoulli polynomials, the generalized -Apostol type Euler polynomials, the generalized -Apostol type Genocchi polynomials of order and level , and the -Bernstein polynomials. PubDate: Mon, 02 Jul 2018 00:00:00 +000

Abstract: We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem. PubDate: Sun, 03 Jun 2018 00:00:00 +000

Abstract: An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions. PubDate: Sun, 03 Jun 2018 00:00:00 +000

Abstract: The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s -function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and -transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters. PubDate: Sun, 03 Jun 2018 00:00:00 +000

Abstract: By a rotational system, we mean a closed subset of the circle, , together with a continuous transformation with the requirements that the dynamical system be minimal and that respect the standard orientation of . We show that infinite rotational systems , with the property that map has finite preimages, are extensions of irrational rotations of the circle. Such systems have been studied when they arise as invariant subsets of certain specific mappings, . Because our main result makes no explicit mention of a global transformation on , we show that such a structure theorem holds for rotational systems that arise as invariant sets of any continuous transformation with finite preimages. In particular, there are no explicit conditions on the degree of . We then give a development of known results in the case where for an integer . The paper concludes with a construction of infinite rotational sets for mappings of the unit circle of degree larger than one whose lift to the universal cover is monotonic. PubDate: Sun, 03 Jun 2018 00:00:00 +000

Abstract: There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a -quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively. PubDate: Tue, 15 May 2018 00:00:00 +000