International Journal Of Nonlinear Analysis And Applications
Volume:7 Issue: 1, Summer - Autumn 2016

In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results.Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of its partial derivative.

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$.Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T: E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (iii) $C_0 (X)$ does not have the fixed point property. We also show that if $A$ is a commutative complex $ mathsf{C}^star$--algebra with nonempty carrier space, then the following statements are equivalent: (i) Carrier space of $ A $ is infinite, (ii) $ A $ is infinite dimensional, (iii) $ A $ does not have the fixed point property. Moreover, we show that if $ A $ is an infinite complex $ mathsf{C}^star$--algebra (not necessarily commutative), then $ A $ does not have the fixed point property.

The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices
uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics. 234(2010) 1387-1394].

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of nonexpansive type multivalued and single valued maps, European J. Pure Appl. Math., 4 (2011) 330-339].

In this paper, we will establish some xed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.

begin{abstract} Using the fixed point method, we prove the generalized Hyers--Ulam--Rassias stability of the following functional equation in multi-Banach spaces: begin{equation} sum_{j = 1}^{n}fBig(-2 x_{j} + sum_{i = 1, ineq j}^{n} x_{i}Big) = (n-6) fBig(sum_{i = 1}^{n} x_{i}Big) + 9 sum_{i = 1}^{n} f(x_{i}).end{equation}end{abstract}

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.

In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lipschitz condition in $L^{p}$.

Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results. Furthermore, other integral inequalities of reverse Minkowski's type are obtained for positive functions resulting in two theorems.

The aim of this paper is to prove some common fixed point theorems for four mappings satisfying $(\psi,\varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.

‎Let $lambda_1,dots,lambda_n$ be positive real numbers such that‎ ‎$sum_{k=1}^n lambda_k=1$‎. ‎We prove that for‎ ‎any positive operators $a_1,a_2,cdots‎, ‎a_n$ in semifinite von‎ ‎Neumann algebra $M$ with faithful normal trace that $t(1)

For every $1\leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.

We introduce variational inequality problems on Hilbert $C^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. Then relation between variational inequalities, $C^*$-valued metric projection and fixed point theory on Hilbert $C^*$-modules is studied.

In this paper, we obtain the general solution and the generalized Hyers--Ulam--Rassias stability in random normed spaces, in non-Archimedean spacesand also in $p$-Banach spaces and finally the stability via fixed point method for a functional equation\begin{align*}&D_f(x_{1},.., x_{m}):= \sum^{m}_{k=2}(\sum^{k}_{i_{1}=2}\sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(\sum^{m}_{i=1, i\neq i_{1},...,i_{m-k+1}} x_{i}-\sum^{m-k+1}_{r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{i=1} x_{i})-2^{m-1} f(x_{1})=0\end{align*}where $m \geq 2$ is an integer number.

In this paper, we prove some coupled coincidence point theorems for mappings with the mixed monotone property and obtain the uniqueness of this coincidence point. Then we providing useful examples in Nash equilibrium.

We classify the paracontact Riemannian manifolds that their Rieman- nian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally sym- metric spaces. Finally we study paracontact Riemannian manifolds satis- fying R(X, ξ).S = 0, where S is the Ricci tensor.

‎In this paper, we discuss about existence of solution for integro-differential system and then we solve it by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in the process of discretizing and we drive a system of algebraic equations with small dimension which it leads to approximate solution with high accuracy. We compare the results with similar works and it guarantees the validity and applicability of this method.

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the fixed points set is nonempty, closed and convex.

In this paper, we introduce the (G-$\psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$

In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to obtain the conditions for which our model exhibits stability around the possible equilibrium points. Besides this a rigorous global stability analysis has been performed for our proposed model by using Li and Muldowney approach (geometric approach). Global stability conditions for the proposed model are described in the form of theorem. This is not a case study, hence the real parameters are not available for this model. However, model may be simulated by using hypothetical set of parameters. Investigation of real parameters for the proposed model is an open problem.

Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$, where $\alpha>-\frac{1}{2}$ and $1 Keywords: Bessel operator, Bessel transform, Bessel generalized translation