Abstract: Abstract In this article, global asymptotic stability of solutions of non-homogeneous differential-operator equations of the third order is studied. It is proved that every solution of the equations decays exponentially under the Routh–Hurwitz criterion for the third order equations. PubDate: 2018-10-10

Abstract: Abstract In this paper, we show the existence of a weak solution to the Maxwell–Stokes type equation with a potential satisfying the Dirichlet condition, under the hypothesis that the domain has no holes, using a version of the de Rham lemma that was proved in our previous paper. We also give the regularity of weak solutions. PubDate: 2018-09-28

Abstract: Abstract In the present paper, we first characterize real hypersurfaces in the complex quadric \(Q^{m}\) by giving an inequality in terms of the scalar curvature and the Mean curvature vector field. We also obtain the condition under which this inequality becomes an equality. Further, we develop two extremal inequalities involving the normalized \(\delta \) -Casorati curvatures and the extrinsic generalized normalized \(\delta \) -Casorati curvatures for real hypersurfaces in \(Q^{m}\) . Finally, we derive the necessary and sufficient condition for the equality in both cases. PubDate: 2018-09-26

Abstract: Abstract In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by introducing two different classes of elementary topical functions. Next, we use this pseudo-metric d to investigate the non-expansivity and some properties of topical functions. Finally, the characterizations of fixed points of topical functions are given, and a relation between the pseudo-metric d and the original norm of the normed linear space X is presented. PubDate: 2018-09-24

Abstract: Abstract Here, we consider the approximation of functions by a large variety of max-product operators under conformable fractional differentiability and using convexity. These are positive sublinear operators. Our study relies on our general results about positive sublinear operators. We derive Jackson-type inequalities under conformable fractional initial conditions and convexity. So our approach is quantitative by obtaining inequalities where their right hand sides involve the modulus of continuity of a high-order conformable fractional derivative of the function under approximation. Due to the convexity assumptions, our inequalities are compact and elegant with small constants. PubDate: 2018-09-01

Abstract: Abstract In this paper, we introduce octadecic functional equation. Moreover, we prove the stability of the octadecic functional equation in multi-normed spaces by using the fixed point method. PubDate: 2018-09-01

Abstract: Abstract Three-dimensional Couette flow of an incompressible Jeffrey fluid is formulated and discussed analytically and graphically. The suction is applied over uniformly moving upper plate and its equivalent deduction by injection at the lower stationary plate. Because of this type of suction/injection, this flow turns into three-dimensional. An analytical method is applied to get main flow velocity, secondary flows velocities and pressure components. Also skin friction components along the main and secondary flow directions have been calculated. The effects of different physical parameters, for example, the Deborah number, suction/injection parameter, the ratio of relaxation time to the retardation time and Reynolds number have been discussed graphically. It is witnessed that the Deborah number plays vital role to control the main flow velocity. PubDate: 2018-09-01

Abstract: Abstract In general the stability of normed algebras is a non hereditary property. We shall prove that second conjugate Banach algebras may be non stable even if the underlying Banach algebra is stable. We shall characterize stability of second conjugate Banach algebras. Finally, we shall study kinds of stability induced on an algebra with an stable second conjugate algebra. PubDate: 2018-09-01

Abstract: Abstract It is known that if \(A\in \mathscr {L}(\mathscr {X})\) and \(B\in \mathscr {L}(\mathscr {Y})\) are Banach operators with the single-valued extension property, SVEP, then the matrix operator \(M_\mathrm{{C}}=\begin{pmatrix} A &{} C \\ 0&{} B \\ \end{pmatrix} \) has SVEP for every operator \(C\in \mathscr {L}(\mathscr {Y},\mathscr {X}),\) and hence obeys generalized Browder’s theorem. This paper considers conditions on operators A, B, and \(M_0\) ensuring generalized Weyl’s theorem and property (Bw) for operators \(M_\mathrm{{C}}\) . Moreover, certain conditions are explored on Banach space operators T and S so that \(T\oplus S\) obeys property (gw). PubDate: 2018-08-27

Abstract: Abstract Let \(\nu _{d,n}: \mathbb {P}^n\rightarrow \mathbb {P}^r\) , \(r=\left( {\begin{array}{c}n+d\\ n\end{array}}\right) \) , be the order d Veronese embedding. For any \(d_n\ge \cdots \ge d_1>0\) let \(\check{\eta }(n,d;d_1,\ldots ,d_n)\subseteq \mathbb {P}^r\) be the union of all linear spans of \(\nu _{d,n}(S)\) where \(S\subset \mathbb {P}^n\) is a finite set which is the complete intersection of hypersurfaces of degree \(d_1, \dots ,d_n\) . For any \(q\in \check{\eta }(n,d;d_1,\ldots ,d_n)\) , we prove the uniqueness of the set \(\nu _{d,n}(S)\) if \(d\ge d_1+\cdots +d_{n-1}+2d_n-n\) and q is not spanned by a proper subset of \(\nu _{d,n}(S)\) . We compute \(\dim \check{\eta }(2,d;d_1,d_1)\) when \(d\ge 2d_1\) . PubDate: 2018-08-24

Abstract: Abstract Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. A dynamic k-coloring is also called a conditional (k, 2)-coloring. The smallest integer k such that G has a dynamic k-coloring is called the dynamic chromatic number \(\chi _d(G)\) of G. In this paper, we investigate the dynamic chromatic number for the line graph of sunlet graph and middle graph, total graph and central graph of sunlet graphs, paths and cycles. Also, we find the dynamic chromatic number for Mycielskian of paths and cycles and the join graph of paths and cycles. PubDate: 2018-08-23

Abstract: Abstract We take a ring \(R = \mathbb F_2+s\mathbb F_2+s^2\mathbb F_2\) . We consider a Gray map on this ring, discuss self-dual codes, define various weight enumerators over the ring, and discuss equivalence class of codes over the ring. We construct self-dual codes of Type I and Type II over the given ring for different lengths. PubDate: 2018-08-20

Abstract: Abstract A class of coupled Schrödinger equations is investigated. First, in the stationary case, the existence of ground states is obtained and a sharp Gagliardo–Nirenberg inequality is discussed. Second, in the energy critical radial case, global well-posedness and scattering for small data are proved. PubDate: 2018-08-06

Abstract: Abstract Assuming the source of energy momentum tensor as perfect fluid, a classification of static cylindrically symmetric spacetimes in f(R) theory of gravity by conformal vector fields (CVFs) is presented. For the classification purpose, we put different conditions on metric coefficients to obtain solutions in f(R) theory of gravity. By means of some algebraic and direct integration techniques, it is shown that the dimension of CVFs for the considered spacetimes turns out to be 4, 5, or 15. PubDate: 2018-08-06

Abstract: Abstract The class of stretch metrics contains the class of Landsberg metrics and the class of R-quadratic metrics. In this paper, we show that a regular non-Randers type \((\alpha , \beta )\) -metric with vanishing S-curvature is stretchian if and only if it is Berwaldian. Let F be an almost regular non-Randers type \((\alpha , \beta )\) -metric. Suppose that F is not a Berwald metric. Then, we find a family of stretch \((\alpha , \beta )\) -metrics which is not Landsbergian. By presenting an example, we show that the mentioned facts do not hold for the Randers-type metrics. It follows that every regular \((\alpha , \beta )\) -metric with isotropic S-curvature is R-quadratic if and only if it is a Berwald metric. PubDate: 2018-08-03

Abstract: Abstract In this paper we study the long-time behavior of solutions for a general class of Langevin-type fractional integro-differential equations. The involved fractional derivatives are either of Riemann–Liouville or Caputo type. Reasonable sufficient conditions under which the solutions are bounded or decay like power functions are established. For this purpose, we combine and generalize some well-known integral inequalities with some crucial estimates. Our findings are supported by examples and special cases. PubDate: 2018-07-26

Abstract: Abstract In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets \({\mathbb {R}}^{\alpha }\, (0<\alpha \le 1)\) of real line numbers. Then, using twice local fractional differentiable mappings that are in absolute value at certain powers generalized strongly m-convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results. PubDate: 2018-07-25

Abstract: Abstract Let R be a prime ring with the extended centroid C and symmetric Martindale quotient ring \(Q_s(R)\) . In this paper we prove the following result. Let \(F: R \rightarrow R\) be a generalized derivation associated with a non-zero derivation d on R and let h be an additive map of R such that \(F(x)x=xh(x)\) for all \(x\in R\) . Then either R is commutative or \(F(x)=xp\) and \(h(x)=px\) where \(p\in Q_{s}(R)\) . PubDate: 2017-12-29

Abstract: Abstract The initial value problem for a coupled nonlinear Schrödinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. In the focusing case, the existence and stability/instability of standing waves are established. Moreover, global well-posedness is discussed via the potential well method. PubDate: 2017-12-15

Abstract: Abstract In this paper, we use techniques and tools from time scale calculus to state and prove many refinements on the discrete Hermite–Hadamard inequality. PubDate: 2017-12-12