In this article، we propose a numerical algorithm for computing price of discrete single and double barrier option under the \emph{Black-Scholes} model. In virtue of some general transformations، the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alternative numerical methods presented in previous papers.

We present symmetric Rogers--Hölder's inequalities on time scales when $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=0$ and $\frac{r}{p}+\frac{r}{q}$ is not necessarily equal to $1$ where $p،$ $q$ and $r$ are nonzero real numbers.

In this paper، the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as Poincar'e mapping، power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.

In this paper، we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.

The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter، this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in some cases using a new hybrid method based on pseudo-spectral collocation in the sense of least square method. Furthermore، the method usages Picard iteration and Newton method to treat nonlinear term in order to obtain unique and multiple solutions of the problem، respectively.

We define a new subclass of univalent function based on Salagean differential operator and obtained the initial Taylor coefficients using the techniques of Briot-Bouquet differential subordination in association with the modified sigmoid function. Further we obtain the classical Fekete-Szego inequality results.

In this paper، we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally، as an application، we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresponding functional equation.

We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end، an application is presented to the study of existence and uniqueness of solutions for a boundary value problem for certain second order ODE and the respective integral equation.

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately multiplicative linear functionals and approximately n-multiplicative linear functionals‎.

‎‎Many authors such as Amini-Harandi‎، ‎Rezapour ‎et al.، ‎Kadelburg ‎et al.‎‎، ‎have tried to find at least one fixed point for quasi-contractions when $\alpha\in[\frac{1}{2}‎، ‎1)$ but no clear answer exists right now and many of them either have failed or changed to a lighter version‎. In this paper‎، ‎we introduce some new strict fixed point results in the set of multi-valued '{C}iri'{c}-generalized weak quasi-contraction mappings of integral type‎. ‎We consider a necessary and sufficient condition on such mappings which guarantees the existence of unique strict fixed point of such mappings. Our result is a partial positive answer for the mentioned problem ‎ which has remained open for many years‎. Also، we give an strict fixed point result of ‎$‎\alpha‎$-‎$‎\psi‎$‎-quasicontractive multi-valued mappings of integral type. Our results generalize and improve many existing results on multi-valued mappings in literature. ‎Moreover‎، ‎some examples are presented to support our new class of multi-valued contractions.

In this paper، by the use of the weight coefficients، the transfer formula and the technique of real analysis، an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover، the equivalent forms، the operator expressions and a few examples are considered.

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of obtained results and few illustrative examples.

Very recently، Kuman et al. [P. Kumam، W. Sintunavarat، S. Sedghi، and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces، Volume 2015، Article ID 350840، 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the continuity of the $b$-metric، but unfortunately، there exists a gap in the proof of the main result. In this note، we point out and fill such gap by making some remarks and offering a new proof for the result. It should be mentioned that our proofs for some key assertions of the main result are new and somewhat different from the original ones. In addition، we also present a result to check the continuity of the $b$-metrics which is found effective and workable when applied to some examples.

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also، as an application، we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a mixed $\leq$-solution.

In this paper، we describe some topological properties of dualistic partial metric spaces and establish some fixed point theorems for weak contraction mappings of rational type defined on dual partial metric spaces. These results are generalizations of some existing results in the literature. Moreover، we present examples to illustrate our result.

Motivated by the $k$-digamma function، we introduce a $k$-extension of the Nielsen's $\beta$-function، and further study some properties and inequalities of the new function.

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the local fractional integral equations.

We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk
$\mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators، Hadamard product and a linear operator. In addition، we obtain some sufficient conditions for the functions belonging to this class and for some of its subclasses

Optimization of the product portfolio has been recognized as a critical problem in industry، management، economy and so on. It aims at the selection of an optimal mix of the products to offer in the target market. As a probability function، reliability is an essential objective of the problem which linear models often fail to evaluate it. Here، we develop a multiobjective integer nonlinear constraint model for the problem. Our model provides opportunities to consider the knowledge transferring cost and the environmental effects، as nowadays important concerns of the world، in addition to the classical factors operational cost and reliability. Also، the model is designed in a way to simultaneously optimize the input materials and the products. Although being to some extent complicated، the model can be efficiently solved by the metaheuristic algorithms. Finally، we make some numerical experiments on a simulated test problem.