Search

Abstract: In this paper, we give some new sufficient conditions for the intersection of orbits with the vertical isoclines of a class of Liénard systems. The results of this paper generalize some previous results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the existence of the solution for a generalized fractional differential equation with non-autonomous variable order operators. In contrast to constant order fractional calculus, some standard relations including composition and sequential derivative rules do not remain correct under this generalization. Therefore, solving such a generalized fractional differential equation requires a different methodology, essential modifications, and generalizations for the basic concepts such as existence and uniqueness of the solution. The main goal of this paper is the proof of existence for the solution of a variable order fractional differential equation which is achieved by presenting four theorems. It is shown that if Lebesgue measurability, the continuity of the nonlinear term, and the conditions of differintegration operation are satisfied, then a solution for the variable order fractional differential equation exists. [Copyright &y& Elsevier]

Abstract: This is a continuation of our paper [M. Liu, K. Wang, Asymptotic properties and simulations of a stochastic logistic model under regime switching, Math. Comput. Modelling 54 (2011) 2139–2154]. First, we establish the sufficient conditions for stochastic permanence which are much weaker than those in our previous paper. Then we study some new asymptotic properties of this model. The lower-growth rate and the upper-growth rate of the positive solution are investigated. The superior limit of the average in time of the sample path of the solution is also estimated. Finally, some simulation figures are introduced to illustrate the main results. Some recent investigations are improved and generalized. [Copyright &y& Elsevier]

Abstract: In 2007, Huang and Zhang [L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] rediscovered normal cone metric spaces and obtained the Banach contraction principle for this setting. Later on, Rezapour and Hamlbarani [Sh. Rezapour, R. Hamlbarani, Some notes on the paper: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008) 719–724] showed that there are non-normal cones and that the assumption of normality is redundant. In this paper, we obtain a generalization of the Banach contraction principle to the class of convex contractions on non-normal cone metric spaces. Our result includes, as special cases, the recent results of Huang and Zhang (2007) and Rezapour and Hamlbarani (2008) . [Copyright &y& Elsevier]

Abstract: This paper studies the stability of switched systems with general nonlinear disturbances. By using generalized Gronwall–Bellman inequalities, we obtain stability results for the systems with arbitrary switching laws. Finally, an example is given to illustrate the effectiveness of the results obtained. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to prove common fixed point theorems for weakly compatible mappings in modified intuitionistic fuzzy metric spaces employing the common limit range property. Illustrative examples are also furnished to support our main results. Our results improve and generalize several previously known fixed point theorems of the existing literature. [Copyright &y& Elsevier]

Abstract: In the present paper, a general recurrence relation for determining the solutions of the time-fractional diffusion equation is obtained with the generalized differential transform method. The obtained relation will help us to solve time-fractional diffusion equations with various external forces and initial conditions. Four illustrative examples are given. [Copyright &y& Elsevier]

Abstract: Common fixed point theorems for -weakly isotone increasing mappings satisfying a generalized contractive type condition under a continuous function with for each and in complete ordered partial metric spaces are proved. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. The empirical log-likelihood ratio statistics are proposed and the nonparametric versions of the Wilk’s theorem are obtained. Furthermore, when the order of the model is 1, we also derive a test statistic to test the stationary–ergodicity based on the conditional least-squares method. Numerical results from simulation studies suggest that the empirical likelihood method is more accurate than the normal approximation-based method of Hwang and Basawa (1998) . Some simulation studies are also conducted to investigate the finite sample performances of the proposed test. [Copyright &y& Elsevier]

Abstract: The concepts of equi-statistical convergence, statistical pointwise convergence and statistical uniform convergence for sequences of functions were introduced recently by Balcerzak et al. [M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328 (2007) 715–729]. In this paper, we use the notion of -statistical convergence in order to generalize these concepts. We establish some inclusion relations between them. We apply our new notion of -equi-statistical convergence to prove a Korovkin type approximation theorem and we show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally, we prove a Voronovskaja type approximation theorem via the concept of -equi-statistical convergence. Some interesting examples are also displayed here in support of our definitions and results. [Copyright &y& Elsevier]

Abstract: In the present paper, by using an almost increasing sequence a known theorem dealing with summability factors of infinite series has been generalized to the summability. This new theorem also includes several new results. [Copyright &y& Elsevier]

Abstract: In this paper, an improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation is used to construct more new exact solutions of a generalized KdV equation with variable coefficients. As a result, seven families of new generalized Jacobi elliptic function-like solutions, soliton-like solutions and trigonometric function solutions of the equation are obtained by using this method, which shows that the general method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics. [Copyright &y& Elsevier]

Abstract: In this paper, the uniform cubic B-spline collocation method is implemented to find the numerical solution of the generalized Black–Scholes partial differential equation. We use the horizontal method of lines to discretize the temporal variable and the spatial variable by means of a -method, ( corresponds to the back-ward Euler method and corresponds to the Crank–Nicolson method), and a cubic B-spline collocation method on uniform meshes, respectively. The method corresponding to is shown to be unconditionally stable and first order accurate with respect to the time variable and second order accurate with respect to the space variable while the method corresponding to is shown to be unconditionally stable and second order accurate with respect to both the variables. Finally, the numerical examples demonstrate the stability and accuracy of the method. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to investigate the demiclosedness principle, the existence theorem, and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. Our results generalize, extend and unify the corresponding results of Dhompongsa and Panyanak [S. Dhompongsa, B. Panyanak, On -convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008) 2572–2579], Osilike and Aniagbosor [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Computer Model., 32 (2000), 1181–1191], Sahu and Beg [D.R. Sahu, I. Beg, Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings, Internat. J. Modern Math., 3(2) (2008), 135–151]. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Using our results, we obtain the mean ergodic theorem for nonexpansive mappings in Hilbert spaces. Our results extend many recent important results. [Copyright &y& Elsevier]

Abstract: In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical physics, engineering and mathematics. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a new class of set-valued vector implicit quasi complementarity problems with corresponding set-valued implicit quasi variational inequality problems. By means of the Fan–KKM theorem, we investigate the nonemptiness and compactness of solution sets of these problems. Our work generalizes and improves some results appeared recently in the literature. [Copyright &y& Elsevier]

Abstract: Zamfirescu [T. ZamfirescuFix point theorems in metric spaces Arch. Math. (Basel) 23 (1972) 292-298], obtained a very interesting fixed point theorem on complete metric spaces by combining the results of S. Banach, R. Kannan and S.K. Chatterjea. In [S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], the author introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we study new extensions of the Zamfirescu theorem to the context of partial metric spaces, and among other things, we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to generalize the functions with bounded Mocanu variation and define the class of functions with bounded Mocanu variation which map the open unit disk onto conic domain. Many interesting properties of these functions are investigated. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain some new existence results of solutions for some Dirichlet impulsive differential problems using critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one nontrivial solution or infinitely many solutions, assuming that the nonlinearity is superquadratic and has a sublinear growth. Our results generalize some existing results and our conditions on the potential are rather relaxed and some existing results in the literature are improved. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a functional generalization of the diamond- integral reverse Hölder inequality on time scales. Some related inequalities are also considered. [Copyright &y& Elsevier]

Abstract: In this paper new explicit expressions for both kinds of Comtet numbers and some interesting special cases are derived. Moreover, we define and study the generalized multiparameter non-central Stirling numbers and generalized Comtet numbers via differential operators. Furthermore, recurrence relations and new explicit formulas for those numbers are obtained. Finally some interesting special cases, new combinatorial identities and a connection between these numbers and some interesting polynomials are deduced. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present some fixed point and coupled fixed point theorems for a nonlinear weakly -contraction type mapping in metric and ordered metric spaces. Also, an example is given to support our results. Our results generalize several well-known results from the current literature. [Copyright &y& Elsevier]

Abstract: In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses restricted variations only for nonlinear terms by generalising the Lagrange multipliers. Consequently, this allows us to use the well known, but ignored, theory of linear ODEs for computing the matrix-valued Lagrange multipliers. In order to validate the newly proposed approach in solving linear and nonlinear systems of differential equations, illustrative examples are presented: it turns out that the use of the generalised Lagrange multipliers is more reliable and efficient. [Copyright &y& Elsevier]

Abstract: In this paper, a general integral identity for convex functions is derived. Then, we establish some new inequalities of the Simpson and the Hermite–Hadamard type for functions whose absolute values of derivatives are convex. Some applications for special means of real numbers are also provided. [Copyright &y& Elsevier]

Abstract: In this paper we study the qualitative behavior of the solutions of the generalized Liénard system and . We present some new conditions under which the solutions of this system are oscillatory. Some examples are used to illustrate our results. [Copyright &y& Elsevier]

Abstract: Making use of a differential operator, we introduce and study a certain class of -valently analytic functions with negative coefficients. In this paper, we obtain numerous sharp results including (for example ) coefficient estimates, distortion theorem, radii of close-to convexity, starlikeness and convexity and modified Hadamard products of functions belonging to the class . Finally, several applications investigate an integral operator, and certain fractional calculus operators are also considered. [Copyright &y& Elsevier]

In this paper, we consider stock price models which are simple generalizations of the binary models. We consider the case when more than two jumps are possible at each trading time. This assumption leads us to incompleteness of the market. Then, on the analogy of the classical case, we study the possible limit laws for the stock price at the terminal date as the number of the trading times goes to infinity and the possible jumps converge to certain limits. We show that normal and Poisson laws and also their certain combinations are possible in this case and give necessary and sufficient conditions for such limit laws. [Copyright &y& Elsevier]

Airborne sonar target recognition involves two key technical issues: target feature extraction and classification. In this paper, the issue designing a feature classifier with high classification accuracy is discussed. Generally, the multilayered feed-forward neural network can be applied to the airborne sonar target feature classification to achieve the high performance requirement. However, neural networks trained by conventional error back-propagation (B-P) learning algorithms suffer from slow convergence rate and inadequate generalization ability. Detailed analysis of the B-P algorithm reveals that these problems are mainly related to the magnitudes of the components of the gradient vector and the direction of the vector associated with the severely ill-conditioned nature of the Hessian matrix of the error function. A fast back-propagation (F-BP) algorithm is therefore developed to accelerate the learning speed of the B-P algorithm. A dynamic training strategy is then applied to the F-BP algorithm to improve the generalization ability. Experiments are carried out for airborne sonar target feature classification using these algorithms. The results show that the performance of the neural network classifier trained with the proposed algorithm is superior to that of traditional B-P algorithm with a seven-fold learning speed advantage over B-P. [Copyright &y& Elsevier]