فهرست مطالب

• Volume:9 Issue:2, 2018
• تاریخ انتشار: 1397/05/24
• تعداد عناوین: 20
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• Rahman Farnoosh* , Hamidreza Rezazadeh, Amirhossein sobhani, Masoud Hasanpour Pages 1-7

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.

Keywords: Discrete Barrier Option, emph{Black-Scholes} Model, Constant Parameters
• Sajid Iqbal *, Muhammad Jibril Shahab Sahir, Muhammad Samraiz Pages 9-19

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.

Keywords: Diamond-$alpha$ integral, Rogers-H?lder's inequalities, time scales
• Djondin Philippe *, Jean, Pierre Barbot Pages 21-31

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.

Keywords: chaos, multicellular chopper, dynamical properties, chaotic attractor, routes to chaos
• Ali Benlabbes, Maamar Benbachir *, Mustapha Lakrib Pages 33-45

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.

Keywords: Caputo fractional derivative, three-point boundary value problem, fixed point theorem on cones
• * Elyas Shivanian, Saeid Abbasbandy Pages 47-57

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.

Keywords: Pseudo-spectral collocation method, Least square method, Newton iteration method, Picard iteration, Chebyshev-Gauss-Lobatto points

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.

Keywords: Univalent functions, Briot-Bouquet differential equation, Integral Operator, Sv{a}lv{a}gean differential operator
• *Hamid Baghani Pages 71-84

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.

Keywords: Fixed point theorem, Weakly Picard operator, O-complete metric space, Selections of multivalued functions
• Hemant Kumar Nashine *, Atul Kumar Sharma Pages 85-109

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.

Keywords: $G$-metric space, Weakly contraction condition, Altering distance function, Compatible mappings, Coincidence point
• Zohre Heidarpour, Esmaeil Ansari, Piri, Hamid Shayanpour, Ali Zohri* Pages 111-116

‎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.

Keywords: ‎strict fixed point, '{C}iri'{c}-generalized weak quasi-contraction, multi-valued mappings, integral type
• Bicheng Yang* Pages 131-143

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.

Keywords: Hardy-Hilbert-type inequality, weight coefficient, equivalent form, operator, norm
• Kishor Kucche*, Pallavi Shikhare Pages 145-159

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.

Keywords: Volterra-Fredholm integrodifferential equations, Ulam-Hyers stability, Ulam-Hyers--Rassias stability, Integral inequality, Picard operator
• Shaoyuan Xu *, Suyu Cheng, Stojan Radenovi? Pages 161-167

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.

Keywords: $b$-metric spaces, $R$-weakly commuting mappings, the continuity concerning the $b$-metric, common fixed points

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.

Keywords: Coupled fixed point, Generalized Kanann mapping, Partially ordered set, Periodic boundary value problem

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.

Keywords: fixed point, dualistic partial metric, Weak contractions
• Kwara Nantomah *, Kottakkaran Sooppy Nisar, Kuldeep Singh Gehlot Pages 191-201

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.

Keywords: Nielsen's $beta$-function, $k$-extension, $k$-digamma function, inequality
• FUAT USTA *, Huseyin Budak, Mehmet Sarikaya Pages 203-214

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.

Keywords: Local fractional calculus, Volterra, Abel’s integral equations, Yang-Laplace transform
• Shahnaz Fakouri, Abdolali Basiri* , Sajjad Rahmani Pages 215-221

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.

Keywords: SAGBI basis, SAGBI algorithm, subalgebra membership problem, homogeneous polynomial
• Abdul Rahman Juma, Mushtaq Abdulhussain, Saba Al, khafaji* Pages 223-230

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

Keywords: Meromorphic $p$-valent functions, Hadamard product, Bazilevi'{c} function, fractional $q$-calculus operators