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A ring R is said to be n-fine if every nonzero element in R can be written as a sum of a nilpotent and n units in R. The class of these rings contains fine rings and n-good rings in which each element is a sum of n units. Fundamental properties of such rings are obtained. One of the main results of this paper is that the m × m matrix ring Mm(R) over any arbitrary ring R is 2-fine. Furthermore, the m × m matrix ring Mm(R) over a n-fine ring R is n-fine. [ABSTRACT FROM AUTHOR]

This paper aims to introduce various concepts of statistical Riemann-Stieltjes sum via the deferred Nörlund summability mean for the sequence of functions as well as the sequence of distribution functions. We first establish some fundamental limit theorems for statistical Riemann-Stieltjes sum in the sequence space. Then over the probability sequence space, we establish some more advanced results. Finally, over both the spaces we establish some inclusion theorems via our proposed mean in association with statistical Riemann-Stieltjes integral. [ABSTRACT FROM AUTHOR]

n this paper we introduce the concepts of Wijsman ρ-statistical convergence of order α and Wijsman strongly ρ-convergence of order α. In addition, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of nonlinear Liouville–Caputo fractional differential equations equipped with a new set of nonlocal boundary conditions involving an arbitrary strip together with two sets of nonlocal multi-points on either part of the strip on the given domain. We emphasize that the boundary conditions considered in this study are formulated with respect to the sum and difference of the unknown functions. We apply the well-known tools of the fixed point theory to derive the main results. Examples are presented for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]

The object of the present paper is to generalize projective curvature tensor of paraKenmotsu manifold with the help of a new generalized (0,2) symmetric tensor Z introduced by Mantica and Suh. Various geometric properties of generalized projective curvature tensor of para-Kenmotsu manifold have been studied. It is shown that a generalized projectively φ symmetric para-Kenmotsu manifold is an Einstein manifold. [ABSTRACT FROM AUTHOR]

In this paper, we give some characterizations on S-curvature in Randers measure spaces, which shows that only the Busemann-Hausdorff volume form can admit a vanishing S-curvature. [ABSTRACT FROM AUTHOR]

In this paper, we prove the stability of Hadamard homomorphisms and Hadamard derivations in Banach algebras. This is applied to investigate Hadamard isomorphisms between Banach algebras. [ABSTRACT FROM AUTHOR]

In the present paper, we proposed a new sequence of summation-integral type operators involving Apostol-Genocchi polynomials. We study some approximation results of the proposed operators using first and second-order modulus of continuity, the global rate of convergence using Voronovskaja-type asymptotic theorem, Lipschitz-type space, and Ditzian-Totik modulus of smoothness. Lastly, we study the weighted approximation. [ABSTRACT FROM AUTHOR]

In this paper, new weighted Hermite-Hadamard type inequalities for differentiable preinvex and prequasiinvex functions are proved. These results generalize many results proved in earlier works for these classes of functions. [ABSTRACT FROM AUTHOR]

In this paper, a new class of multi-agent systems with addictive and multiplicative measurement noises under Markovian switching topologies is introduced. Some sufficient conditions of average consensus to the systems are also established under consideration. First, based on the continuous-time Markov chain with finite modes, the time-varying topologies of the considering system is figured. Then, the mean square average consensus for the multi-agent systems with a time-varying gain under the time-varying topologies and the Markov chain is studied. Finally, the example and simulation results are given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and M be an R-module. The aim of this paper is to introduce the notion of S-copure submodules and investigate some properties of this class of modules. We say that a submodule N of M is S-copure if there exists an s ∈ S such that s(N :M I) ⊆ N + (0 :M I) for every ideal I of R. [ABSTRACT FROM AUTHOR]

In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials. [ABSTRACT FROM AUTHOR]

In this paper, some new estimations of Hermite-Hadamard-Fejér type inequalities for higher order differentiable preinvex functions are established via fractional integral operators. The main motivation point of the study is that our findings, which include generalized preinvex functions for Hermite-Hadamard-Fejér type inequalities by means of fractional integral operators, are the rare results in the literature. The coincidence of the special cases of the our main theorems with the earlier works in the literature is also demonstrated as a verification of our results. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale sequences of random variables via deferred Cesaro ` mean. We then establish an inclusion theorem concerning the relation between these two beautiful and potentially useful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale sequence over a Banach space. Moreover, we demonstrate that our theorems effectively extend and improve most (if not all) of the previously existing results (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are stronger than their traditional and statistical versions. [ABSTRACT FROM AUTHOR]

Consider a simple connected graph G = (V(G),E(G)), where V(G) represents the vertex set and E(G) represents the edge set respectively. A subset W of V(G) is called a resolving set for a graph G if for every two distinct vertices x, y ∈V(G), there exist some vertex w ∈W such that d(x,w) 6= d(y,w), where d(u, v) denotes the distance between vertices u and v. A resolving set of minimal cardinality is called a metric basis for G and its cardinality is called the metric dimension of G, which is denoted by β(G). A subset D of V(G) is called a doubly resolving set of G if for every two distinct vertices x, y of G, there are two vertices u, v ∈ D such that d(u, x) - d(u, y) 6= d(v, x) - d(v, y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by ψ(G). In this paper, we determine the minimal doubly resolving sets for antiprism graphs denoted by An with n ≥ 3 and for Mobius ladders denoted by Mn, for every even positive integer n ≥ 8. It has been proved that ψ(An) = 3 for n ≥ 3 and ψ(Mn) = ( 3, if n ≡ 0 or 4 (mod 8) 4, if n ≡ 2 or 6 (mod 8) for every even positive integer n ≥ 8. [ABSTRACT FROM AUTHOR]

This paper presents new geometric viewpoints to Chen chaotic system. Firstly, the existence of two nontransverse homoclinic orbits in Chen system is rigorously proved beyond the classical parameters. Secondly, combined with the theory of tangent bundle, a new geometric viewpoint is given to explore chaos mechanism of Chen system. The fundamental geometric definition of tangent bundle and the essential role of nonlinear connection between the tangent space and the base space are described. By introducing the geometrical viewpoints of second order system governed by Lie-Poisson equation, some geometric invariants of Chen system can be obtained. Furthermore, the torsion tensor as one of the geometric invariants is obtained, and it gives the geometrical interpretation to the chaotic behaviour of Chen system. Finally, the torsion tensor of Chen system and Lorenz system are also compared. The obtaining results show that torsion tensor change will lead the Chen system from periodic to chaotic, which is not found in Lorenz system. [ABSTRACT FROM AUTHOR]

In this paper we study the regular prism tilings and construct ball packings by geodesic balls related to the above tilings in the projective model of Nil geometry. Packings are generated by action of the discrete prism groups pq21. We prove that these groups are realized by prism tilings in Nil space if (p,q) = (3,6),(4,4),(6,3) and determine packing density formulae for geodesic ball packings generated by the above prism groups. Moreover, studying these formulae we determine the conjectured maximal dense packing arrangements and their densities and visualize them in the projective model of Nil geometry. We get a dense (conjectured locally densest) geodesic ball arrangement related to the parameters (p,q) = (6,3) where the kissing number of the packing is 14, similarly to the densest lattice-like Nil geodesic ball arrangement investigated by the second author in [11]. [ABSTRACT FROM AUTHOR]

In this paper, we establish new weighted integral inequalities for differentiable hconvex and quasi-convex functions. Applications of our findings to continuous random variables and approximation of integrals are given. [ABSTRACT FROM AUTHOR]

In this paper, we establish the stability of n-cubic functional equations in Lipschitz spaces and as a consequence we give the stability of cubic functional equations. [ABSTRACT FROM AUTHOR]

This paper includes four finite element methods which are based on quadratic, cubic, quartic and quintic trigonometric B-spline functions for space discretization and Crank-Nicolson method for time discretization, to be achieved the numerical solution of the Schrodinger equation (SE). The algorithms obtained by different degrees trigonometric B-spline Galerkin methods are new for getting numerical solution of the SE. To see the accuracy of the proposed methods, two numerical experiments are investigated and the comparison of the methods are given in the test problem section. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (p,ϕh)-convex functions and present some properties and representation of such functions. Finally, a version of Hermite Hadamard-type inequalities for (p,ϕh)-convex functions are established. [ABSTRACT FROM AUTHOR]

In this paper, some new weighted Simpson's type integral inequalities are presented for the class of harmonically-preinvex functions by using power-mean integral inequality and Holder's integral inequality. [ABSTRACT FROM AUTHOR]

In this paper, we study the complex dynamical behaviors of a discrete-time SIR epidemic model. Analysis of the model demonstrates that the Diseases Free Equilibrium (DFE) point is globally asymptotically stable if the basic reproduction number is less than one while the Endemic Equilibrium (EE) point is globally asymptotically stable if the basic reproduction number is greater than one. The results are further substantiated visually with numerical simulations. Furthermore, numerical results demonstrate that the discrete model has more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behaviors. The maximum Lyapunov exponent and chaotic attractors also confirm the chaotic dynamical behaviors of the model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I. A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babeş-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babeş-Bolyai Univ. ClujNapoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of nonlinear operators-the class of general historydependent operators. These are the operators defined on spaces of functions endowed with a structure of Banach space (the case of bounded interval of time) or Frechet space (the case of unbounded interval of time). We state and prove various properties of such operators, including fixed point properties. Moreover, we also study several classes of differential equations in Banach spaces, for which we our previous results can be applied. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main results. [ABSTRACT FROM AUTHOR]

This paper deals with a problem of a wave equation with p-Laplacian and logarithmic nonlinearity term. Firstly, local existence of weak solutions have been obtained by applying Banach fixed theorem. Later, the finite-time blow up of the solutions have been obtained for negative initial energy. [ABSTRACT FROM AUTHOR]

Matrix factorizations have been widely used in recent years, especially in engineering problems, to facilitate performance-requiring computations. In this paper, we investigate some interesting relationships between some combinatorial matrices such as Pascal matrix, Stirling matrices and k-order Fibonacci matrices. We give factorizations and inverse factorizations of the Pascal and Stirling matrices via k-order Fibonacci matrices. Moreover, we derive various combinatorial properties by using relationships between these matrices. Finally, compared to previous studies, we present more general results for specific values of k. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the following linear 2m-th order parabolic equation ∂tu+(-1) m ∑ N k=1 ∂ 2m xk u = f, subject to Dirichlet type condition ∂ l νu = 0, l = 0,1,...,m-1, on the lateral boundary, where m is a positive integer. The right-hand side f of the equation is taken in the Lebesgue space L p, 1 < p < +∞. The problem is set in a domain of the form Q = (t, x1,..., xN) ∈ R N+1 : 0 ≤ q x 2 1 +...+x 2 N < t α with α > 1/2m. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Diophantine equation Pn -3a = ν and find all ν having at least two representations. In the proof of the main theorem, we use a version of the Baker-Davenport reduction method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study modified two-step iteration process for a pair of quasi-nonexpansive mapping and asymptotically quasi-nonexpansive mapping in the intermediate sense. We also establish some strong convergence theorems and a weak convergence theorem for this iteration scheme and mappings in the framework of real Banach spaces. The results presented in this paper extend, improve and generalize some previous results from the existing literature (see for example [1, 3, 5-7, 9-13]). [ABSTRACT FROM AUTHOR]

In this paper, we prove some iterated convergence theorems to fixed points of self mappings satisfying Z-type conditions and Z-operators by considering the base space as a real linear n(> 1)-normed space. We also establish some common fixed point theorems for quadruple of self mappings satisfying certain weak conditions and Φ- contraction. The paper also demonstrates a way to construct convergence and fixed point theorems in real linear n-normed spaces as base space. [ABSTRACT FROM AUTHOR]

Space-like surfaces with special second fundamental forms have been an important tool in the study of pseudo-Riemannian manifolds. This paper focuses on adapting some theorems of Riemannian geometry in the large to the study of geometry of space-like surfaces of pseudo-Riemannian manifolds, specifically, various comparison theorems that use sectional and Ricci curvatures. The purpose of this paper is to establish a global geometry of complete spacelike totally umbilical and maximal surfaces in pseudo-Riemannian manifolds. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of contraction: the almost local contractions. Then, we prove the existence and uniqueness of a fixed-point for local almost contractions in two cases: with constant and variable coefficients of contraction. [ABSTRACT FROM AUTHOR]

In this paper we study the modified Hadamard product properties of certain class of analytic functions with varying arguments defined by Ruscheweyh derivative. The obtained results are sharp and they improve known results. [ABSTRACT FROM AUTHOR]

In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of obtained expressions to the other recursive sequences. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. Most of the results are sharp. [ABSTRACT FROM AUTHOR]

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove a tripled common fixed point theorem of Suzuki type for a pair of hybrid mappings in metric spaces. Our result generalizes and modifies several comparable results in the literature. We also provide an example to support our theorem. [ABSTRACT FROM AUTHOR]

S. Radeleczki in 2002 raised the open problem of the characterization of those atomistic complete lattices whose classification lattices are geometric. This paper solves the problem for the finite cases. [ABSTRACT FROM AUTHOR]

Recently, a new definition of fractional derivative called as the conformable fractional derivative which based on limits introduced by Khalil et al (2014). Later, Abdeljawad (2015) improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel's formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce new q-Stancu-Kantorovich operators and to study some of their approximation properties. A convergence theorem using the well known Bohman- Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. Furthermore, a Voronovskaja type theorem is also proven. [ABSTRACT FROM AUTHOR]

In this paper, a one-sided condition is given to recover (C,α) summability of a sequence from its (A)(C, α+1) summability. Our result extends and generalizes the well known classical Tauberian theorems given for Abel and Cesàro summability methods. [ABSTRACT FROM AUTHOR]

In the present paper we investigate commutativity of *-prime ring R, which satisfies certain differential identities on *-ideals of R. Some results already known for prime rings on ideals have also been deduced. Finally, we provide several examples to justify that various restrictions imposed in the hypotheses of our theorems are not superfluous. [ABSTRACT FROM AUTHOR]

The paper is concerned with the semisimplicity of smash products of generalized quantum commutative algebras in weak Hopf algebra setting. Let H be a weak Hopf algebra over a field k and A any semisimple and generalized quantum commutative weak Yetter-Drinfeld H-module algebra. It is shown that A♯H is semisimple if and only if A is a projective left A♯Hmodule. Applying results to quasitriangular (weak) Hopf algebras is considered. [ABSTRACT FROM AUTHOR]

In this paper, we use the order relation on uniform spaces defined by [5] to introduce the notion of compatibility of mappings in an ordered uniform space and use this notion to establish coupled coincidence point theorems to ordered uniform space. An example is also given. [ABSTRACT FROM AUTHOR]

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of contractions of Berinde-Suzuki type on a partial metric space. Moreover, using our results, as application we obtain a new characterization of partial metric 0-completeness. Finally, we give a typical application of fixed point methods to integral equation, by using our results. [ABSTRACT FROM AUTHOR]

Let us consider a non-self mapping T : A → B, where A and B are two nonempty subsets of a metric space (X,d). The aim of this paper is to solve the nonlinear programming problem that consists in minimizing the real valued function x → d(x,T x), where T belongs to a new class of non-self mappings. In especial case, existence and uniqueness of fixed point for Kannan type self mappings are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, the convergence of Mann iterative process with errors for generalized Lipschitz ϕ-quasi-accretive operators is proved in uniformly smooth Banach spaces. Our results improve the corresponding results of Chidume et al.[2]. [ABSTRACT FROM AUTHOR]

In this paper, we prove a general theorem dealing with generalized absolute convolution Cesàro mean summability factors under weaker conditions by using a general class of increasing sequences instead of an almost increasing sequence. Some new results have also been obtained. [ABSTRACT FROM AUTHOR]