International Journal Of Nonlinear Analysis And Applications
Volume:6 Issue: 4, Winter - Spring 2015

In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential equation. Finally an existence of extremal random solution is obtained in between the given upper and lower random solutions.

In cite{p}, Park introduced the quadratic $rho$-functional inequalities begin{eqnarray} && |f(x+y)+f(x-y)-2f(x)-2f(y)| && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 flef (frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumber end{eqnarray} where $rho$ is a fixed complex number with $|rho|and begin{eqnarray} && left|2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right| && qquad le |rho(f(x+y)+f(x-y)-2f(x)-2f(y))|, nonumber end{eqnarray} where $rho$ is a fixed complex number with $|rho| In this paper, we prove the Hyers-Ulam stability of the quadratic $rho$-functional inequalities (0.1) and (0.2) in $beta$-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of quadratic $rho$-functional equations associated with the quadratic $rho$-functional inequalities (0.1) and (0.2) in $beta$-homogeneous complex Banach spaces.

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have that $$ |L|=|widehat{L}|,;forall; ; L in {mathcal{L}}^{s}(^{n}X);. $$ If the previous relation holds for every $L in {mathcal{L}}^{s}left(^{n}Xright)$, then spaces ${mathcal{P}}left(^{n}Xright)$ and $L in {mathcal{L}}^{s}(^{n}X)$ are isometric. We can also study the same problem using Fr$acute{e}$chet derivative.

In this investigation, attempts have been made to solve two-dimension nonlinear viscous flow between slowly expanding or contracting walls with weak permeability by utilizing a semi analytical Akbari Ganji''s Method (AGM). As regard to previous papers, solving of nonlinear equations is difficult and the results are not accurate. This new approach is emerged after comparing the achieved solutions with numerical method and exact solution. Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. Results illustrate, this method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods. Ruge-Kutta numerical method, Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) have been applied to make this comparison. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.

This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.

The dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and Poincar''{e} sections. Also, we employed perturbation methods such as Lindstedt''s method to obtain the frequency-amplitude relation of escape oscillator.

This paper presents dynamic portfolio model based on the Merton''s optimal investment-consumption model, which combines dynamic synthetic put option using risk-free and risky assets. This paper is extended version of methodological paper published by Yuan Yao (2012) cite{26}. Because of the long history of the development of foreign financial market, with a variety of financial derivatives, the study on theory or empirical analysis of portfolio insurance focused on how best can portfolio strategies be used in minimizing risk and market volatility. In this paper, stock and risk-free assets are used to replicate options and to establish a new dynamic model to analyze the implementation of the dynamic process of investors'' actions using dynamic replication strategy. Our results show that investors'' optimal strategies of portfolio are not dependent on their wealth, but are dependent on market risk and this new methodology is broaden in compare to paper of Yuan Yao (2012).

In the paper we establish some new results depending on the comparative growth properties of composition of entire functions using relative $L^{ast}$-order (relative $L^{ast}$-lower order) as compared to their corresponding left and right factors where $Lequiv Lleft(rright) $ is a slowly changing function.

In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath might be called their definitive versions. Also, we show that there are examples which show that our main theorems are genuine generalizations of theorem 3.1 and 3.2 of cite{R} [M.A. Miandaragh, M. Postolache, S. Rezapour, textit{Approximate fixed points of generalized convex contractions}, Fixed Point Theory and Applications 2013, 2013:255.]

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they sued from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre polynomials, expansion functions. Trigonometric functions and etc. In the proposed method we obtain all of the solutions of the non-linear integral equations. For showing ability and validity proposed method we compare our results with some works.

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination- and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

Let X be a vector space over a field K of real or complex numbers. We will prove the superstability of the following Golab-Schinzel type equation f(x + g(x)y) = f(x)f(y); x; y 2 X; where f; g are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product. Our result refers to papers by Chudziak and Tabor (J. Math. Anal. Appl. 302 (2005) 196–200), Jab lo´nska (Bull. Aust. Math. Soc. 87 (2013), 10–17) and Rezaei (Math. Ineq. Appl., 17 (2014), 249–258).

In this paper, by applying three functional operators the previous results on the(Poisson) variance of the external profile in digital search trees will be improved. We study the profile built over $n$ binary strings generated by a memoryless source with unequal probabilities of symbols and use a combinatorial approach for studying the Poissonized variance, since the probability distribution of the profile is unknown.