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In this paper, we study the following two-dimesional system of difference equations ... where the parameters a;b; c;d and the initial values x i; y i, i 2 f1;2;3;4;5;6g, are real numbers. We show that some subclasses of nonlinear two-dimensional system of difference equations are solvable in closed form. We also describe the forbidden set of solutions of the system of differ- ence equations. Some numerical examples are given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

We study the problem of finding the common element of the set of fixed points of two nonexpansive mappings in Hilbert spaces. Some previous attempts in this direction make some restrictive assumptions which may be difficult to check in practice on the generated sequence. In this paper, we introduce a viscosity S-iteration scheme for finding the common fixed point of two nonexpansive mappings. Under some very mild conditions, we obtain a strong convergence theorem for the sequence generated by our algorithm. We apply our main result to approximating common fixed points of nonexpansive semigroups. We also provide numerical examples to support our main results and illustrate the efficiency and effectiveness of our algorithm by comparing with some existing algorithms in literature. This work generalizes and improves some existing works in the literature in this direction. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some existence results for multivalued contraction mappings in the context of an O-complete orthogonal metric space (not necessarily complete metric space). Also, we provide a partial solution to Reich’s problem for multivalued orthogonal contraction mappings and extend Mizoguchi-Takahashi’s point theorem. In addition, we give an example to demonstrate the applicability of our established results. We study the solution of a differential equation and its Ulam’s stability as an application of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the generalized differential transform method (GDTM) is used to solve certain class of nonlinear time-fractional diffusion equation. An efficient recurrence relation is obtained to solve this problem. Some numerical examples are given for different class of derivative orders which are analyzed numerically for the specified examples. [ABSTRACT FROM AUTHOR]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, by using invariants of Riemann and general solutions of Euler–Poisson– Darboux–Riemann equations, a new class of exact solutions of von Karman’s equation in the nonlinear theory of gas dynamics is given. [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]

In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. Then using the Fourier method and contraction mappings principle, the existence and uniqueness theorem for auxiliary problem is proved. Further, on the basis of the equivalency of these problems the existence and uniqueness theorem for the classical solution of the considered inverse coefficient problem is proved for the smaller value of time. [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]

n the paper we consider canonical almost geodesic mappings π2(e), e = ±1, of spaces with affine connection onto 2-symmetric, 3-symmetric and m-symmetric spaces. The main equations for the mappings have been obtained as closed systems of PDEs of Cauchy type in covariant derivatives. We have found the maximum numbers of essential parameters which the general solutions of the systems depend on. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some Hermite-Hadamard type inequalities for uniformly convex functions with respect to geodesic in Hadamard space. Also, we give some application of these functions in means. [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]

The aim of this paper is to study the ∗-identities with a pair of generalized derivations on ∗-ideals of prime rings with involution. In particular, we prove that if a noncommutative prime ∗-ring admit two generalized derivations F and G such that [F (x),G(x* )] = 0 for all x ∈ I, where I is a nonzero ∗-ideal of R, then there exists λ ∈ C such that F = λG. Finally, we provide an example which shows that the primeness of R is crucial in our results. [ABSTRACT FROM AUTHOR]

In this paper, we extend the result of Romaguera [21] with the aid of best proximity point theory on partial metric spaces by considering the approach of Haghi et al. [9], and so celebrated Boyd-Wong fixed point theorem [7]. We first introduce two concepts called generalized proximal BW-contraction and generalized best BW-contraction. Then, we obtain some best proximity point theorems for such mappings. To illustrate the effectiveness of our results, we provide some nontrivial and interesting examples. Finally, unlike homotopy applications existing in the literature, we present for the first time an application of the best proximity result to the homotopy theory. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the oscillation of numerical solutions for a nonlinear delay differential equation which is generalized from a delay Lotka-Volterra type single species population growth model. By studying the corresponding difference scheme of the equation discretized by θ-method, forward Euler method and backward Euler method, some sufficient conditions under which the numerical solutions oscillate are obtained. Furthermore, we prove that the positive non-oscillatory numerical solutions tend to the equilibrium of the original differential equation. Finally, some numerical experiments are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a two dimensional discrete-time predator-prey system with weak Allee effect, affecting the prey population, is considered. The existence of the positive fixed points of the system and topological classification of coexistence positive fixed point are examined. By using the bifurcation theory, it is shown that the discrete-time predator-prey system with Allee effect undergoes flip and Neimark-Sacker bifurcations depending on the parameter a. The parametric conditions for existence and direction of bifurcations are investigated. Numerical simulations including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the system are performed to validate analytical results. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the considered system. Finally, the OGY feedback control method is implemented to stabilize chaos existing in the system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of integration with respect to a given derivation on a lattice. More precisely, we give the definitions of integrable elements of a lattice and their integral sets. We investigate several characterizations and properties of integrations on a lattice. Also, we give a lattice structure to the family of integral sets with respect to a given integration. Further, we provide a representation theorem for the lattice of fixed points of an isotone derivation based on the family of integral sets. As an application of this notion of integration, we use the integrable elements of a Boolean lattice to determine the necessary and sufficient conditions under which a linear differential equation on this Boolean lattice has a solution. [ABSTRACT FROM AUTHOR]

The novelty of our paper is to establish results on asymptotic stability of mild solutions in pth moment to Riemann-Liouville fractional stochastic neutral differential equations (for short Riemann-Liouville FSNDEs) of order α ∈ (1/2,1) using a Banach's contraction mapping principle. The core point of this paper is to derive the mild solution of FSNDEs involving Riemann-Liouville fractional time-derivative by applying the stochastic version of variation of constants formula. The results are obtained with the help of the theory of fractional differential equations, some properties of Mittag-Leffler functions and asymptotic analysis under the assumption that the corresponding fractional stochastic neutral dynamical system is asymptotically stable. [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 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]

In this paper, we establish Hermite-Hadamard inequalities for subadditive functions, and we give some related inequalities according to Hermite-Hadamard inequalities, which generalized the previously published results. [ABSTRACT FROM AUTHOR]

In this paper, we study combinatoric convolution sums involving divisor functions. First, we establish some explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli polynomials. Second, we show a formula of the fourth order of convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli polynomials. [ABSTRACT FROM AUTHOR]

In this paper, the initial-value problem for a linear second order delay differential equation is considered. To solve this problem numerically, an appropriate difference scheme is constructed by using the method of integral identities which contains basis functions and interpolating quadrature rules with weight and remainder term in integral form. Besides, the method is proved to be first-order convergent in discrete maximum norm. The numerical illustration provided support the theoretical results. Finally, the proposed method is compared with the implicit Euler method. [ABSTRACT FROM AUTHOR]

In this paper, by the differential operator we give some congruences and new proof for some known congruence concerning the Bell polynomials, derangement polynomials and r-Lah polynomials. [ABSTRACT FROM AUTHOR]

The paper introduces the notions of boundedness and convergence with speed for difference sequences, and characterizes certain matrix classes associating the sets of such classes of sequences involving the operator Δ and two speeds λ = (λk) and µ = (µk) ... The results obtained in this paper should easily extendible to difference sequences of higher orders, and even, in combination with multipliers. [ABSTRACT FROM AUTHOR]

In this paper, a new type of stability for nonlinear systems of differential equations called practical ψγ-exponential asymptotic stability, is presented. Some sufficient conditions for practical ψγ-exponential asymptotic stability are provided by using Lyapunov theory. These results generalize fundamental well known results for practical exponential asymptotic and ψ-exponential asymptotic stability for nonlinear time-varying systems. In addition, these results are using to investigate the practical ψγ-exponential asymptotic stability problem of nonlinear perturbed system and cascade systems. The last part is devoted to the study the problem of practical ψγ-exponential asymptotic stabilization for some classes of nonlinear systems with delayed perturbation. [ABSTRACT FROM AUTHOR]

In this paper, half inverse spectral problem for diffusion operator with jump conditions dependent on the spectral parameter and discontinuity coefficient is considered. The half inverse problems is studied of determining the coefficient and two potential functions of the boundary value problem its spectrum by Hocstadt-Lieberman and Yang-Zettl methods. We show that two potential functions on the whole interval and the parameters in the boundary and jump conditions can be determined from the spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite approximate controllability of fractional semilinear differential equations involving the Hilfer derivative. We show that if the linear part is approximate controllable, then under suitable conditions the semilinear system is finite approximate controllable. [ABSTRACT FROM AUTHOR]

In this paper, the operator denoted by Dm : A → A, is defined by Dm[ f ](z) = (1 λ)Rm[ f ](z)+lLm[ f ](z), z 2 U, a differential-integral operator, where Rm is Ruscheweyh differential operator and Lm is Libera integral operator. By using the operator Dm the class of univalent functions denoted by M(m,λ,a), 0 ≤ λ ≤ λ 0 ≤ λ a < 1, is defined and several differential subordinations are studied. [ABSTRACT FROM AUTHOR]

In this paper, complex differential equations from first and second order with constant coefficients are solved using reduced differential transform method (RDTM). Such equations were previously solved by other methods. While obtaining a solution with these methods, the solution was reached by dividing the equation into real and imaginary parts. With the RDTM used in this study, we found that the solution can be reached without dividing the real and imaginary parts of the equation. An iteration relation is given for the solution of such equations. In addition, a variable coefficient equation was solved with RDTM. [ABSTRACT FROM AUTHOR]

In this paper we introduce the classes Tn (p,λ,A,B) and Kn (p,λ,µ,m,A,B) and derive distortion inequalities of the functions belonging to class Kn (p,λ,µ,m,A,B). Further we apply to the (n,δ)- neighborhoods of functios in the class Kn (p,λ,µ,m,A,B). [ABSTRACT FROM AUTHOR]

The paper is about investigating the uniform convergence conditions of spectral expansions of continuous functions in terms of root functions of a spectral problem with the same eigenparameter in the second-order differential equation and depending on quadratically in one of the boundary conditions on a closed interval. [ABSTRACT FROM AUTHOR]

In this paper we study functional-differential equations on the semi-axis, which are non-linear with respect to the phase variables and linear with respect to the control. Sufficient conditions for existence of optimal control in terms of the right-hand side and the quality criterion are obtained. Relation between the solutions of the problems on infinite and finite intervals is studied and results that about these connections are proven. [ABSTRACT FROM AUTHOR]

In this paper, the approximate solutions by using the undetermined fuzzy coefficients method and the exact solutions by using the Hukuhara differentiability of second-order fuzzy linear boundary value problems with constant coefficients are investigated. Thus, comparisons of the found solutions are given. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

This paper is concerned with a Shimizu-Morioka model with constant delays. Its stability of the equilibrium is investigated and the existence of Hopf bifurcations is demonstrated by analyzing the associated characteristic equation. Furthermore, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the center manifold theory and the normal form method. Finally, special attention is paid to numerical simulations in order to verify the theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the convergence of the fitted mesh method applied to singularly perturbed Volterra delay-integro-differential equation. Our mesh comprises a special nonuniform mesh on the first subinterval and uniform mesh on another part. Error estimates are obtained using difference analogue of Gronwall's inequality with delay. A numerical test that confirms the theoretical results is presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete population model and obtain a couple of criteria to guarantee our model being stable, including the global attractor, the extreme stability, and the periodicity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new generalized inverses of matrices, namely, the hi;mi-core inverse and the (j, m)-core inverse. The (i, m)-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler [1] and the core-EP inverse defined by Manjunatha Prasad and Mohana [10]. The (j, m)-core inverse of a complex matrix extends the notions of the core inverse and the DMP-inverse defined by Malik and Thome [9]. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials Fnk (x, s, q) and the incomplete q-Lucas polynomials Lnk (x, s, q), respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the (p, q)-analogues (with 0 < q < p ≥ 1) by applying some obvious parametric variations, the additional parameter p being redundant. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the umbral representation of the geometric polynomials wxn; = wn (x) to derive some properties involving these polynomials. Furthermore, for any prime number p and any polynomial f with integer coefficients, we show (f (wx))p≡ f (wx) (mod p) and we give other curious congruences. [ABSTRACT FROM AUTHOR]

In the first part of this work we present some basics about the connection of exponential dichotomy and Floquet-theory. Then we study some stability notions of linear differential equations based on the concept of the exponential and ordinary dichotomy. More precisely we shall show that the definition of the asymptotical (Lyapunov-) stability can be formulated by using the exponential dichotomy. In the main part of the paper we consider parameter dependent non-autonomous linear and autonomous nonlinear systems which have at a certain value of the parameter an asymptotically stable solution. Then we examine the question how much the parameter can be changed such that the solution remains asymptotically stable. Finally, we study the orbital stability of periodic solutions of autonomous systems applying the previous results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with 2p-order Hamiltonian systems with impulsive effects. We investigate the variational structure associated to this system. In addition, we obtain some results of multiple solutions for asymptotically linear 2p-order Hamiltonian systems via variational methods and critical point theorems. Meanwhile, some examples are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

We consider the following second order impulsive differential equation with delays ... In this paper we obtain sufficient conditions of nonpositivity of Green's functions for impulsive differential equation. All results are formulated in the form of theorems about differential inequalities. It should be noted that the sign-constancy of the coefficients bj (t) was assumed in all the literature devoted to impulsive functional differential equations. One of the main purposes of this work is to propose a technique allowing us to avoid these assumptions. [ABSTRACT FROM AUTHOR]