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In this paper, we deal with the form of the solutions and the periodicity character of the following systems of nonlinear difference equations of order two Zn+1 = Zntn-1/±tn ± tn-1, tn+1 = tnZn-1/±Zn ± Zn-1, where the initial conditions Z-1, Z0, t-1 and t0 are nonzero real numbers. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear di¤erence equation... where the parameters α,β,γ, a; b; c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l,k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the dynamics of a system of fourth-order rational difference equations... where the parameter A is arbitrary positive real number and the initial conditions x-3,x-2,x-1,x0,y-3,y-2,y-1,y0 are arbitrary nonnegative real numbers. By using new iteration method for the more general nonlinear difference equations and inequality skills, we establish some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for this nonlinear system. Numerical examples to the difference system are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this article we study the existence of solutions and some of their qualitative behavior of the following rational nonlinear difference equation xn+1 = axn-(2k+1)/ b + cxn-kxn-(2k+1) , n = 0, 1, ..., where a, b and c are real numbers, k is a non-negative integer number and the initial conditions x-2k-1, x-2k , ..., x-1, x0 are arbitrary non-negative real numbers. Also, the solutions of some special cases of the equation under consideration will be obtained. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the form of the solutions and the periodicity character of the following systems of nonlinear difference equations of order two zn+1=zn+tn-l/±tn±tn-1,tn+1=tnzn-l/±zn±zn-l where the initial conditions z-1, z0, t-1 and t0 are nonzero real numbers. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to investigate the global stability of the solutions, the boundedness and the periodic character of the nonlinear difference equationxn+1 = βxn+βxn-l+γxn-k + axnxn-k/bxn + cxn-l + dxn-k, n = 0, 1, ..., where the parameters α, β, γ, a, b, c and d are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, x0 are positive real numbers where s = max{l, k}. Some numerical examples will be given to explicate our results. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the dynamics of a system of fourth-order rational difference equations xn+1=xn-3-yn-1/A+xn-3yn-1,yn+1=yn-3-xn-1/A+yn-3xn-1, n=0,1,..., where the parameter A is arbitrary positive real number and the initial conditions x-3,x-2,x-1,x0,y-3,y-2,y-1,y0 are arbitrary nonnegative real numbers. By using new iteration method for the more general nonlinear difference equations and inequality skills, we establish some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for this nonlinear system. Numerical examples to the difference system are given to verify our theoretical results. [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 xn+1 = Axnxn-3/Bxn + Cxn-2 and xn+1 =Axnxn-3/ Bxn - Cxn-2 , 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]

This paper is devoted to investigate the dynamics of the rational difference equation xn+1 =xn-1/A + Bxnxn-1 with arbitrary initial conditions A and B as nonzero real numbers. The solution is obtained and analytical study and asymptotic behavior are investigated. The forbidden set is determined. The existence of periodic and oscillatory solutions are discussed. Our results are illustrated with numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we solve the additive ρ-functional equations f(x + y) - f(x) - f(y) = ρ(2f(x + y/2)-f(x)-f(y)), (0.1) 2f(x + y) - f(x) - f(y) = ρ (f(x + y) - f(x) - f(y)) ; (0.2) 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]

In this paper, we first investigate and present several sets of sufficient conditions for Carathéodory functions in the open unit disk U. We then apply the main results proven here in order to derive some conditions for starlike functions in U. Relevant connections with various known results are also considered. [ABSTRACT FROM AUTHOR]

We approximate fixed points of some iterative methods on a generalized Banach space setting. Earlier studies such as [5, 6, 7, 12] require that the operator involved is Fréchet-differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of these methods to include generalized fractional calculus and problems from other areas. Some applications include generalized fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences. [ABSTRACT FROM AUTHOR]

In this paper, we solve the following additive p-functional inequalities N(f(x + y) - f(x) - f(y), t) ⩽ N (P ( 2f ( x + y / 2 ) - f(x) - f(y) ), t ) (0.1) and N ( 2f ( x + y / 2 ) - f(x) - f(y), t ) ⩽ N(p (f(x + y) - f(x) - f(y)) , t) (0.2) in fuzzy normed spaces, where p is a fixed real number with ∣p∣ < 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]

The main objective of this paper is to study the periodic character and the global stability of the positive solutions of the difference equation xn+1 = axn + bxn-k + cxn-l - dxn-s/exn-s - αxn-t, n = 0, 1, ..., where the parameters a, b, c, d, e and α are positive real numbers and the initial conditions x-σ, x-σ+1, ..., x-1, x0 are positive real numbers where σ = max{s, t, k,}. Some numerical examples were given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the solutions of the following rational difference equation with big order xn+1 = axn-l + bxn-k + cxn-s + dxn-t/exn-s + fxn-t 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 x0 are positive real numbers where r = max(l, k, s, t). [ABSTRACT FROM AUTHOR]

In [1] and [6] Marx and Strohhäcker have proved that if f ∊ A is a convex function, then it has the property of starlikeness of order 1/2 . In [5, Theorem 9.5.6], P. T. Mocanu extended this result to the class A2 for a convex function of order - 1/2 . In this paper we extend the results proven by Marx and Strohhäcker and by P. T. Mocanu and we'll prove that, if the function f ∊ An, n ≥ 3, is a close-to-convex function, then it is starlike of order 1/2 . [ABSTRACT FROM AUTHOR]

In this paper, we introduce the following useful functional equations: f(x+y) + f(x-2y) + f(y-x)= f(x) f (∑i=1p xi/p-1) + p∑fi=2p ∑j=1,j≠ixj- pxi/p-1) + f(∑i=2pxi-x1/p-1) = f(x1)and prove the superstability and the Hyers-Ulam stability of (r; s; t)-J*-homomorphisms, associated with those, by using the fixed point method and the direct method. [ABSTRACT FROM AUTHOR]

In this paper, by considering Barnes-type Narumi polynomials of the second kind as well as poly-Cauchy polynomials of the second kind, we define and investigate the mixed-type polynomials of these polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities. [ABSTRACT FROM AUTHOR]