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There are many publications on theoretical analysis of deterministic difference equations and stochastic differential equations. However, relatively few theoretical papers are published to consider the positivity of solutions of discrete-time stochastic difference equations (DSDEs), and no theoretical papers investigate the global stability of nontrivial solutions of DSDEs with nonlinear terms. In this paper, we consider a DSDE model that is a generalization of two-dimensional nonlinear models of stochastic predator-prey interactions, and show the positivity and global stability of the nontrivial solutions by using our new discretized version of the It^o formula. In addition, our results are compared with those of continuous-time stochastic differential equations and discrete-time deterministic difference equations. Numerical simulations are introduced to support the results. [ABSTRACT FROM AUTHOR]

The "oldest quartic" functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x - 2y) = 4[f(x + y) + f(x - y)] - 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic functional equations, and establish fundamental formulas for the general solution of such functional equations and for "Ulam stability" of pertinent quartic functional inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Apollonius type additive func tional equation: ... and investigate homomorphisms between C*-ternary algebras and derivations on C*-ternary algebras and homomorphisms between JB*-triples and derivations on JB*-triples under general control functions. Our paper extend the results obtained by Park and Rassias [Choonkil Park and Themistocles M. Rassias, Homomorphisms in C*-ternary algebras and JB*-triples, J. Math. Anal. Appl. 337(2008), 13{20]. [ABSTRACT FROM AUTHOR]

In this paper, we address the stability analysis of within-host Chikungunya virus (CHIKV) infection models with antibodies. We incorporate two modes of infections, attaching a CHIKV to a host monocyte, and contacting an infected monocyte with an uninfected monocyte. The global stability analysis of the equilibria are established using Lyapunov method. The existence and global stability of the steady states are determined by the basic reproduction number R0. We have proven that the CHIKV-free equilibrium E0 is globally asymptotically stable when R0 ≤ 1; and the infected equilibrium E1 is globally asymptotically stable when R0 > 1: The theoretical results are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Hyers-Ulam stability of Cauchy's mean value points which is a extended and generalized version of I. R. Peter and D. Popa's theorem [10] and then, as applications, we obtain Hyers-Ulam stability results of Lagrange's mean value points which refine the result of P. Gāvrutā, J. Huang and Y. Li [5]. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following new type cubic-quartic (CQ) functional equation where λ ≥ 2 is a fixed integer. We investigate the general solution of the functional equation, and then, using the fixed point method, we prove some stability results for this functional equation in matrix fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

In this paper we consider the behavior of a special case of piecewise linear systems of difference equations with initial condition in first quadrant. We found a necessary condition that the solutions become equilibrium point or periodic with prime period 4 without using stability theorems. We constructed inductive statement to represent the behavior of the system and we apply useful lemmas in the proof of main theorem. [ABSTRACT FROM AUTHOR]

The principal purpose of this paper is to present some qualitative behavior of the following fourth order di¤erence equation:... where the parameters a; b; c and d are positive real numbers and the initial conditions x-3; x-2; x-1 and x0 are arbitrary non zero real numbers. [ABSTRACT FROM AUTHOR]

In this paper, we study the qualitative behavior of the rational recursive sequences ... where the initial conditions are arbitrary real numbers. Also, we give the numerical examples of some cases of difference equations and obtained some related graphs and figures using by Matlab. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the local stability of the equilibrium points, global attractor, boundedness and the form of the solutions for the following equations ... where the coefficients A, B and C are real positive numbers, and the initial conditions x -3, x -2, x -1, x0 are arbitrary non zero real numbers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the following new additive s-functional inequalities ||f(x - y) + f(y) + f(-x)|| ≤ ||s (f(x + y) - f(x) - f(y)) k; (0.1) ||kf(x + y) - f(x) - f(y)|| ≤ ||s (f(x - y) + f(y) + f(-x)) k; (0.2) where s is a fixed complex number with |s| < 1, and prove the Hyers-Ulam stability of linear derivations on Banach algebras associated to the additive s-functional inequalities (0.1) and (0.2). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concept of a Menger probabilistic normed Riesz space. We study some properties of these spaces and compare normed Riesz spaces with Menger probabilistic normed Riesz spaces. Next, we investigate the Hyers-Ulam stability of lattice homomorphisms in Menger probabilistic normed Riesz spaces. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability analysis of a virus dynamics model with CTL immune response and with both cell-to-cell and virus-to-cell transmissions. The model contains three types of distributed time delays. The existence and global stability of all steady states of the model are determined by two parameters, the basic reproduction number (R0) and the CTL immune response activation number (R1). By using suitable Lyapunov functionals, we show that if R0 ≤ 1, then the infection-free steady state E0 is globally asymptotically stable; if R1 ≤ 1 < R0, then the CTL-inactivated infection steady state E1 is globally asymptotically stable; if R1 > 1, then the CTL-activated infection steady state E2 is globally asymptotically stable. Numerical simulations are conducted to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we show the Ulam-Hyers stability and Ulam-Hyers-Rassias stability criterion for nonlinear Hadamard fractional relaxation differential equations on compact and unbounded time intervals. More explicit Ulam-Hyers stability and Ulam-Hyers-Rassias results are presented by virtue of estimation of Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the global stability of the positive solutions, the boundedness and the periodic character of the difference equation xn+1 = Axn + Bxn ¡ l + Cxn ¡ k + γxn ¡ k/Dxn ¡ s + Exn ¡ t, n=0, 1, ..., where the parameters A, B, C, D, E,γ ∊ (0,∞) and the initial conditions x¡ σ, x¡ σ+1,..., x¡1, x0 are positive real numbers where σ= max{l, k, s, t}. Numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the local and the global stability of the solutions, the periodic character and the boundedness of the difference equation xn+1 = axn + bxn-1 + α + cxn-2/β + dxn-2 where the parameters β, α, a, b, c and d are positive real numbers and the initial conditions x-2, x-1 and x0 are positive real numbers. Some numerical examples will be given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate essentially stability theory for the fuzzy differential equations in the quotient space of fuzzy numbers by Lyapunov-like functions. By using the differential inequalities and the comparison principle for Lyapunov-like functions, we give some sufficient criterias for the asymptotically stability, equi-asymptotically stability and uniformly asymptotically stability of the trivial solution of the fuzzy differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of a fractional differential equation of order α ∈ (1,2) with certain boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, using the direct and fixed point methods, we investigate the generalized Hyers-Ulam stability of the quintic functional equation. [ABSTRACT FROM AUTHOR]

In this paper, we solve the quadratic ρ-functional equations f (x+ y)+ f (x− y)− 2f (x)− 2f (y)(0.1)= ρ(2f(x+y/2)+ 2f(x−y/2)− f (x)− f (y)),where ρ is a fixed non-Archimedean number or a fixed real or complex number with ρ≠− 1, 2,and2f(x+y/2)+ 2f(x−y/2)− f (x)− f (y)(0.2)= ρ (f (x+ y)+ f (x− y)− 2f (x)− 2f (y)),whereρ is a fixed non-Archimedean number or a fixed real or complex number with ρ≠− 1, 1/2.Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functionalequations (0.1) and (0.2) in non-Archimedean Banach spaces and in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, using the fixed point method, we investigate the Hyers-Ulam stability of homomor- phisms in non-Archimedean random C*-algebras and non-Archimedean random Lie JC*-algebras and of derivations on non-Archimedean random C*-algebras and non-Archimedean random Lie JC*-algebras related to the generalized Cauchy-Jensen additive functional equation. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the existence, uniqueness and stability of solution for stochastic functional differential equations driven by G-Brownian motion (in short G-SFDEs). The existence-and-uniqueness theorem is established for G-SFDEs under non-Lipschitz condition and weakened linear growth condition. We have used the Picard approximation scheme, Gronwall's inequality, Bihari's inequality and Burkholder-Davis-Gundy (in short BDG) inequalities to develop the existence theory for the above mentioned stochastic dynamical systems. In addition, the mean square stability of solutions for these systems has been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we solve the additive (α, β,)-functional equation f(x) + f(y) + 2f(z) = αf(β,(x + y + 2z)); (0.1) where α, β, are β,xed real or complex numbers with α ≠ 4 and αβ, = 1. Using the β,xed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α, β,)-functional equation (0.1) in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following functional equation af(x + y) + bf(x - y) + cf(y - x) = (a + b)f(x) + cf(-x) + (a + c)f(y) + bf(-y) for a fixed real numbers a; b; c with a = b + c and a ≠ 0. We study the fuzzy version of the generalized Hyers-Ulam stability for it in the sense of Mirmostafaee and Moslehian. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the generalized Hyers-Ulam stability of the additive functional inequality ‖(ax + by + cz) + f(bx + ay + bz) + f(cx + cy + az)‖ ≤ ‖(a + b + c)f(x + y + z)‖ in vector Banach space, where a ≠ b ≠ c 2 R are fixed points with 3 > ∣a + b + c∣. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam stability of a fractional di erential equation of order α∊(1; 2) with certain boundary conditions. [ABSTRACT FROM AUTHOR]

A mapping f : X × X → Y is called additive-quadratic if f satisfies the system of equations { f(x + y, z) = f(x, z) + f(y, z), f(x, y + z) + f(x, y - z) = 2f(x, y) + 2f(x, z): In this paper, using the fixed point method, we prove the Hyers-Ulam stability in matrix fuzzy normed spaces associated to the following additive-quadratic functional equation f(x + y, z + w) + f(x + y, z - w) = 2f(x, z) + 2f(x,w) + 2f(y, z) + 2f(y,w) for all x, y, z,w ϵ X. [ABSTRACT FROM AUTHOR]

In this paper, we solve the additive ρ-functional equations ... where ρ is a fixed non-Archimedean number or a fixed real or complex number with ρ ≠ 1. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ- functional equations (0.1) and (0.2) in non-Archimedean Banach spaces and in Ba- nach spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some results concerning the hyperstability of the generalized Cauchy functional equation f(ax + by) = Af(x) + Bf(y) + C Namely, we show, under some assumptions, that a function satisfying the equation approxi- mately must be actually a solution to it. [ABSTRACT FROM AUTHOR]

An optimal control method for cholera epidemic with time delay is developed in this paper. We first explore the local stability of both the disease-free and endemic equilibria of ODE model by analyzing the corresponding characteristic equations, whose global stability is established by constructing two suitable Lyapunov functionals. Furthermore, in order to, we use optimal control theory via the Pontryagin's Maximum Principle and genetic algorithm based on the forward and backward difference approximation to minimize the infected populations and the costs. Numerical simulations demonstrate that the time delay and multiple optimal controls can bring different effects on the dynamics behaviors of the proposed cholera model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a fixed point theorem for a mapping without the condition of bounded orbit in a modular space, whose induced modular is lower semi-continunous. Using this fixed point theorem, we prove the generalized Hyers-Ulam stability for an additive-cubic functional equation in modular spaces without Δ2-conditions and the convexity. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the generalized Hyers-Ulam stability of homomorphisms in C*-algebras and Lie C*-algebras and also of derivations on C*-algebras and Lie C*-algebras for an 4-variable additive functional equation. [ABSTRACT FROM AUTHOR]

Let A and B be real ternary Banach algebras. An additive mapping f: (A, [ ]A) → (B, [ ]B) ismcalled a ternary Jordan homomorphism if f([x, x, x]A) = [f(x),f(x),f(x)]B for all x∊A. In this paper, we investigate the stability and superstability of ternary Jordan ring homomorphisms in ternary Banach algebras by using the fixed point method. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation xn+1 = axn-1l + . . ., n = 0, 1, ..., where the initial conditions x-r, x-r+1, x-r+2, ..., x0 are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive p-functional inequalities ... in fuzzy normed spaces, where p is a fixed real number with |ρ| < 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive p-functional inequalities (0.1) and (0.2) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the quadratic ρ-functional inequalities ... where ρ is a fixed non-Archimedean number with |ρ| < 1/2. Furthermore, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive-quadratic ρ-functional inequalities ... where ρ is a fixed complex number with |ρ| < 1, and ... where p is a fixed complex number with |p| < 1/2, and prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) and (0.2) in β-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive-quadratic p-functional equations associated with the additive-quadratic p-functional inequalities (0.1) and (0.2) in β-homogeneous complex Banach spaces. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the periodic character and the global stability of the positive solutions of the difference equation ... where the parameters a, b, c, d, e and a are positive real numbers and the initial conditions x --&#963, x-σ+1, ···, x-1, xo, xo are positive real numbers where σ = max {s, t, l, k} Some numerical examples were given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we use a fixed point method to prove the stability of ternary m-derivations on ternary Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the solutions of the following rational difference equation with big order ... where the parameters a, b, c, d, e and f are positive real numbers and the initial conditions X -- r, X -- r+1 ···, X --1 and xo are positive real numbers where r = max(l, k, s, t}. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following cubic p-functional inequality Il f (2x + y) + f (2x - y) - 2f (x + y) - 2f (x - y) - 12f (x)|| where p is a fixed complex number with | ρ| < 2, and the quartic ρ-functional inequality ||f (2x + y) + f (2x - y) - 4 f (x + y) - 4f (x - y) - 24f (x) + 6f(y)||... where ρ is a fixed complex number with | ρ| < 2. Using the direct method, we prove the Hyers-Ulam stability of the cubic ρ-functional inequality (0.1) and the quartic ρ-functional inequality (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following quadratic p-functional inequalities ... where ρ is a fixed non-Archimedean number with |ρ| < 1/4, and ... where ρ is a fixed non-Archimedean number with |ρ| < |8|. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic ρ functional inequalities (0.1) and (0.2) in non-Archimedean Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we present a fixed point method to prove the Hyers-Ulam stability of the system of Euler-Lagrange quadratic-quartic functional equations ... for all numbers a and b with a + b ∉ {0, ± 1 }, ab + 2 ∉ 2(a + b)² and ab(a - b)² + 4 ∉ 4(a + b)4 in Archimedean and non-Archimedean Banach spaces and we show that the approximation in non- Archimedean Banach spaces is better than the approximation in (Archimedean) Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized Hyers-Ulam stability for the following quadratic functional equation.... Here Gf is a functional operator of f . We consider some sufficient conditions on Gf which can be applied easily for the generalized Hyers-Ulam stability, and illustrate some new functional equations by using them. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate Hyers-Ulam stability of the following lattice preserving functional equation on Riesz space with fixed point method: ||F(τx V ηy) -- τF(x) V ηF(y)|| ≤ φ(τx V ηy, τx Λ ηy), where X is a Banach lattice and φ : X × X ↑ X is a mapping such that φ(x,y)≤(τη)α/2 φ(x/τ,y/η) for all τ,η ≥ 1 and α ∈[0,1/2). [ABSTRACT FROM AUTHOR]

In this paper, we solve the quadratic ρ-functional inequalities... where ρ is a number with |ρ| < 1 and ... where ρ is a number with |ρ| < 1/2 2. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in normed spaces. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of non-normal solid cone and some fixed point theorems for generalized Lipschitz contractive mappings in cone metric spaces over Banach algebras. Our results greatly generalize the main work by Xu and Radenović (Fixed Point Theory and Applications, 2014, 2014: 102). Moreover, we verify the P property and T-stability of Picard's iteration. Further, we give an example to illustrate that our works are never a copy of metric results in the literature. [ABSTRACT FROM AUTHOR]

In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; κ) quadratic mapping. The other authors of this research area have established important results also on functional inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we study the global properties of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model contains two types of intracellular discrete time delays to describe the time required for viral contacting an uninfected target cell and viral emission. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R0 (the basic infection reproduction number) and R1 (the antibody immune response activation number) which are sufficient to determine the global behavior of the model. The global asymptotic stability of the equilibria of the model has been proven by using direct Lyapunov method and applying LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]

We obtain in this paper the analytical forms of the solutions for the following di¤erence equations ... where the initial conditions are arbitrary real numbers. Also, we study the dynamics behavior of the solutions of the considered equations. [ABSTRACT FROM AUTHOR]