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The subject of this paper is an analytic approximate method for a class of stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions but behave like a polynomials. More precisely, equations from the observed class have unique solutions with bounded moments and their coefficients satisfy polynomial condition. Approximate equations are defined on partitions of a time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. The rate of Lp convergence increases when degrees in Taylor approximations of coefficients increase. At the end of the paper, an example is provided to support the main theoretical result.

The aim of this paper is to correct results from the published paper: A companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications, Filomat 30:13 (2016), 3601-3614.

In the paper, we study the value distribution of the differential polynomial Afn f(k) + Bf n+1 -1, where f is a transcendental meromorphic function and n(? 2),k(?2) are positive integers. We prove an inequality for the Nevanlinna characteristic function T(r,f) in terms of reduced counting function only. The result of the paper not only improves the result due to Q.D. Zhang [J. Chengdu Ins. Meteor., 20(1992), 12-20], also partially improves a recent result of H. Karmakar and P. Sahoo [Results Math., (2018),73:98].

In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of nonspreading mappings and a finite family of nonexpansive multivalued mappings in Hadamard space. We state and prove strong and ? convergence theorems of the proposed iterative process. The results obtained in this paper extend and improve some recent known results.

The aim of this paper is to study the difference gap (in short, D-gap) function and error bounds for a class of the random mixed equilibrium problems in real Hilbert spaces. Firstly, we consider regularized gap functions of the Fukushima type and Moreau-Yosida type. Then difference gap functions are established by using these terms of regularized gap functions. Finally, the global error bounds for random mixed equilibrium problems are also developed. The results obtained in this paper are new and extend some corresponding known results in literatures. Some examples are given for the illustration of our results.

Multisplitting methods are useful to solve differential-algebraic equations. In this connection, we discuss the theory of matrix splittings and multisplittings, which can be used for finding the iterative solution of a large class of rectangular (singular) linear system of equations of the form Ax = b. In this direction, many convergence results are proposed for different subclasses of proper splittings in the literature. But, in some practical cases, the convergence speed of the iterative scheme is very slow. To overcome this issue, several comparison results are obtained for different subclasses of proper splittings. This paper also presents a few such results. However, this idea fails to accelerate the speed of the iterative scheme in finding the iterative solution. In this regard, Climent and Perea [J. Comput. Appl. Math. 158 (2003), 43-48: MR2013603] introduced the notion of proper multisplittings to solve the system Ax = b on parallel and vector machines, and established convergence theory for a subclass of proper multisplittings. With the aim to extend the convergence theory of proper multisplittings, this paper further adds a few results. Some of the results obtained in this paper are even new for the iterative theory of nonsingular linear systems.

The problems considered in this paper are described in polyhedral multi-valued mappings for higher order(s-th) discrete (PDSIs) and differential inclusions (PDFIs). The present paper focuses on the necessary and sufficient conditions of optimality for optimization of these problems. By converting the PDSIs problem into a geometric constraint problem, we formulate the necessary and sufficient conditions of optimality for a convex minimization problem with linear inequality constraints. Then, in terms of the Euler-Lagrange type PDSIs and the specially formulated transversality conditions, we are able to obtain conditions of optimality for the PDSIs. In order to obtain the necessary and sufficient conditions of optimality for the discrete-approximation problem PDSIs, we reduce this problem to the form of a problem with higher order discrete inclusions. Finally, by formally passing to the limit, we establish the sufficient conditions of optimality for the problem with higher order PDFIs. Numerical approach is developed to solve a polyhedral problem with second order polyhedral discrete inclusions.

In this paper, we introduce the notion of exceptional family for the system of implicit generalized order complementarity problems in vector lattice. We present some alternative existence results of the solutions for the system of implicit generalized order complementarity problems via topological degree aspects. The new developments in this paper generalize and improve some known results in the literature.

This paper adds in our hands a different analytic numeric method to solve a class of fuzzy fractional differential equations (FFDEs) based on the residual power series method (RPSM) under strongly generalized differentiability. The analytic and approximate solutions are provided with the series form according to their parametric form. The new method explained in the current paper has a lot of advantages as follows: First, its nature is global according to the obtainable solutions along with being able to solve numerous problems such as mathematical, physical and engineering ones. Second. It is easily noted that it is precise, needs few efforts to have the required results achieved, alongside being developed for nonlinear problems and cases. As for the third advantage, it can be said that any point in the interval of interest will be possibly picked, in addition, to have the approximate solutions applied. Fourth, the method does not need the variables discretization, also it is not implemented by computational round of errors. At last, the results reached in the current paper show several features concerning the new method such as potentiality, generality and superiority to handle such problems arising in physics and engineering as well.

In this paper we study the pointwise convergence and convergence in L1-norm of double trigonometric series whose coefficients form a null sequence of bounded variation of order (p,0),(0,p) and (p,p) with the weight (jk)p-1 for some integer p > 1. The double trigonometric series in this paper represents double cosine series, double sine series and double cosine sine series. Our results extend the results of Young [9], Kolmogorov [4] in the sense of single trigonometric series to double trigonometric series and of M?ricz [6,7] in the sense of higher values of p.

In the paper minimization of a Lagrange type cost functional over the feasible set of solutions of higher order differential inclusions with endpoint constraints is studied. Our aim is to derive sufficient conditions of optimality for m th-order convex and non-convex differential inclusions. The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called ?endpoint? conditions. Here the basic apparatus of locally adjoint mappings is suggested. An application from the calculus of variations is presented and the corresponding Euler-Poisson equation is derived. Moreover, some higher order linear optimal control problems with quadratic cost functional are considered and the corresponding Weierstrass-Pontryagin maximum principle is constructed. Also at the end of the paper some characteristic features of the obtained result are illustrated by example with second order linear differential inclusions.

In this paper, a sufficient condition in order to have C-udomonotone property for multifunctions is presented. By applying a special minimax theorem and KKM theory some existence results of solutions of a generalized variational inequality problem are established. Some examples in order to illustrate the main results are given. The results of this paper can be considered as extension and improvement of some articles in this area.

In this paper, we continue investigation of the problem considered in our earlier works. The paper deals with an optimal control problem for an ordinary differential equation with integral boundary conditions that generalizes the Cauchy problem. The problem is investigated the case when Pontryagin?s maximum principle is degenerate. Moreover, the second order optimality conditions are derived for the considered problem.

This paper is concerned with a stochastic non-autonomous Lotka-Volterra cooperative model with impulsive effects. The main purpose of this paper is to explore the existence of periodic solution of the system provided that the coefficients of the system are continuous periodic functions. By constructing appropriate Lyapunov functions and using the theory of Khasminskii, sufficient conditions under which the existence of the periodic solution of the system are obtained. Our results illustrate that the existence of the periodic solution has close relations with the white noise and the impulsive perturbations.

In this paper, we study two parametric weak and strong vector quasivariational inequality problems of the Minty type. The stability properties of the exact solution sets and approximate solution sets for these problems such as the upper semicontinuity, the lower semicontinuity, the Hausdorff lower semicontinuity, the continuity and the Hausdorff continuity are obtained. The results presented in the paper improve and extend the main results in the literature.

In this paper, we consider the system of generalized variational-like inclusion problems in semi-inner product spaces. We define a class of (H,?)-?-monotone operators and its associated class of generalized resolvent operators. Further, using generalized resolvent operator technique, we give the existence of solution of the generalized variational-like inclusion problems. Furthermore, we suggest an iterative algorithm and give the convergence analysis of the sequences generated by the iterative algorithm. The results presented in this paper extend and unify the related known results in the literature.

In this paper, the complete moment convergence for the weighted sums of extended negatively dependent (END, in short) random variables is investigated. Some general conditions to prove the complete moment convergence are provided. The results obtained in the paper generalize and improve the corresponding ones for some dependent sequences.

In this paper, we present some results on the complete convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables by using the Rosenthal-type maximal inequality, Kolmogorov exponential inequality and the truncation method. The results obtained in the paper extend the corresponding ones for weighted sums of negatively associated random variables with identical distribution to the case of arrays of rowwise NSD random variables without identical distribution.

The purpose of this paper is to introduce and study an iterative scheme for solving the split feasibility problems in the setting of $p$-uniformly convex and uniformly smooth Banach spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper extends some recent results done by Jitsupa Deepho and Poom Kumam [Jitsupa Deepho and Poom Kumam, A Modified Halpern’s Iterative Scheme for Solving Split Feasibility Problems, Abstract and Applied Analysis, Volume 2012, Article ID 876069, 8 pages] and some others.

In this paper, an accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and Chen [6], Niu et al. [18] and Xie et al. [25]. Theoretical analysis shows that the new algorithm will converge to the true solution for any initial value under certain assumptions. Finally, three numerical examples are given to verify the eficiency of the accelerated algorithm proposed in this paper.

This paper represents a generalization of the stability result on the Euler-Maruyama solution, which is established in the paper M. Milosevic, Almost sure exponential stability of solutions to highly nonlinear neutral stochastics differential equations with time-dependent delay and Euler-Maruyama approximation, Math. Comput. Model. 57 (2013) 887 - 899. The main aim of this paper is to reveal the sufficient conditions for the global almost sure asymptotic exponential stability of the ?-Euler-Maruyama solution (? ? [0, 1/2 ]), for a class of neutral stochastic differential equations with time-dependent delay. The existence and uniqueness of solution of the approximate equation is proved by employing the one-sided Lipschitz condition with respect to the both present state and delayed arguments of the drift coefficient of the equation. The technique used in proving the stability result required the assumption ? ?(0, 1/2], while the method is defined by employing the parameter ? with respect to the both drift coefficient and neutral term. Bearing in mind the difference between the technique which will be applied in the present paper and that used in the cited paper, the Euler-Maruyama case (? = 0) is considered separately. In both cases, the linear growth condition on the drift coefficient is applied, among other conditions. An example is provided to support the main result of the paper.

In this paper, two kinds of system of fuzzy differential inclusions are introduced and studied. An existence of the solutions for one system of fuzzy differential inclusions is proved by using continuous selection theorem. An existence of the solutions for another system of fuzzy differential inclusions is also proved by employing the fixed point theorem in the generalized metric space. The results presented in this paper improve and extend some known results concerned with the multivalued Cauchy problem and fuzzy differential inclusions.

In this paper, we study the symmetric generalized quasi-variational inclusion problems. Then, we establish some existence theorems of solution sets for these problems. Moreover, the stability of solutions for these problems are also onbtained. Finally, we apply these results to symmetric vector quasi-equilibrium problems. The results presented in this paper improve and extend the main results in the literature. Some examples are given to illustrate our results.

In recent years, the AOR iterative method has been proposed for solving absolute value equations. This method has two parameters ? and ?. In this paper, we intend to find the optimal parameters of this method to improve convergence rate by suitable optimization techniques. Meanwhile, the convergence of the optimized AOR iterative method is discussed. It is both theoretically and experimentally demonstrated efficiency of the optimized AOR iterative method in contrast with the AOR and SOR methods.

In this paper, we establish some existence results for higher-order nonlinear fractional differential inclusions with multi-strip conditions, when the right-hand side is convex-compact as well as nonconvexcompact values. First, we use the nonlinear alternative of Leray-Schauder type for multivalued maps. We investigate the next result by using the well-known Covitz and Nadler?s fixed point theorem for multivalued contractions. The results are illustrated by two examples.

In this paper, we introduce a flexible extension of the generalized weighted exponential distribution which is called four-parameter generalized weighted exponential (FGWE) distribution. Theoretical properties of this model including the mode, median, moment generator function, moments, mean deviations, mean residual life, coefficients of skewness and kurtosis, hazard function, survival function, Bonferroni and Lorenz curves, reliability probability, entropy measures and stochasting ordering are derived and studied in details. We develop the maximum likelihood estimators of the unknown parameters and their corresponding asymptotic confidence intervals. A simulation study and a real world application are also worked out to assess the maximum likelihood estimators and to illustrate the applicability of the proposed distribution in practice.

In this paper, we consider the method for solving the finite minimax problems. By using the exponential penalty function to smooth the finite minimax problems, a new three-term nonlinear conjugate gradient method is proposed for solving the finite minimax problems, which generates sufficient descent direction at each iteration. Under standard assumptions, the global convergence of the proposed new three-term nonlinear conjugate gradient method with Armijo-type line search is established. Numerical results are given to illustrate that the proposed method can efficiently solve several kinds of optimization problems, including the finite minimax problem, the finite minimax problem with tensor structure, the constrained optimization problem and the constrained optimization problem with tensor structure.

In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on the Krasnoselskii?s fixed point theorem, we perform investigations on the existence of solutions to the system of stochastic differential equations with random impulses. We apply the integral inequality of Gronwall type to the equations and study their Ulam-Hyers-Rassias stability.

In this paper, under suitable conditions we employ the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel?skii fixed point theorem to show the existence of positive solutions for a system of nonlinear singular Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions. Some examples are given to illustrate our main results.

Convergence of real sequences, as well as complex sequences are studied by B. Liu and X. Chen respectively in uncertain environment. In this treatise, we extend the study of almost convergence by introducing double sequences of complex uncertain variable. Almost convergence with respect to almost surely, mean, measure, distribution and uniformly almost surely are presented and interrelationships among them are studied and depicted in the form of a diagram. We also define almost Cauchy sequence in the same format and establish some results. Conventionally we have, every convergent sequence is a Cauchy sequence and the converse case is not true in general. But taking complex uncertain variable in a double sequence, we find that a complex uncertain double sequence is a almost Cauchy sequence if and only if it is almost convergent. Some suitable examples and counter examples are properly placed to make the paper self sufficient.

In this paper, a modified orthogonal linear spline (OL-spline) is used for the numerical solution of a coupled nonlinear inverse reaction-diffusion problem to determine the unknown boundary conditions. The convergence properties of the new linear combination are obtained. A quasi-linearization technique is utilized to linearize the nonlinear term in the equations. This process produces a linear system of equations which can be solved easily. Using the new inequalities, error estimation and convergence of the proposed method are investigated. Two numerical examples are given to demonstrate the computational efficiency of the method and also the experimental convergence rate of examples are obtained.

We utilize the definition of a fractional integral operators, which was presented by Ahmad et al., to investigate a general fractional-type identity with a parameter. We establish certain parameterized fractional integral inequalities based on this identity, and provide two examples to illustrate the obtained results. Also, these results derived in this paper are applied to the estimations of q-digamma function, divergence measures and cumulative distribution function, respectively.

In this paper, we introduce a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and the variational inclusion problem with two accretive operators. We obtain a strong convergence theorem in the setting of Banach spaces. In terms of this theorem, we establish the strong convergence result for solving the fixed point problem (FPP) of an asymptotically nonexpansive mapping and the variational inequality problem (VIP) for an inverse-strongly monotone mapping in the framework of Hilbert spaces. Finally, this result is applied to deal with the VIP and FPP in an illustrating example.

In this paper, we propose a new explicit iteration method using shrinking projection for solving the split best proximity point and equilibrium problems. We prove its strong convergence under some suitable conditions in Hilbert spaces. A numerical example are given to illustrate the effectiveness of the proposed algorithm.

The main object of this paper is to construct a new Durrmeyer variant of the ?-Bernstein type operators which have better features than the classical one. Some results concerning the rate of convergence in terms of the first and second moduli of continuity and asymptotic formulas of these operators are given. Moreover, we define a bivariate case of these operators and investigate the approximation degree by means of the total and partial modulus of continuity and the Peetre?s K-functional. A Voronovskaja type asymptotic and Gr?ss-Voronovskaja theorem for the bivariate operators is also proven. Further, we introduce the associated GBS (Generalized Boolean Sum) operators and determine the order of convergence with the aid of the mixed modulus of smoothness for the B?gel continuous and B?gel differentiable functions. Finally the theoretical results are analyzed by numerical examples.

In this paper, we consider a nonlinear differential system with initial and multi - point boundary conditions. The existence of solutions is proved by using the Banach contraction principle or the Krasnoselskii?s fixed point theorem. Furthermore, the existence of positive solutions is also obtained by applying the Guo-Krasnoselskii?s fixed point theorem in cones. As a consequence of the Guo-Krasnosellskii?s fixed point theorem, the multiplicity of positive solutions is established.

In this paper, a compact alternating direction implicit (ADI) method has been developed for solving two-dimensional Riesz space fractional diffusion equation. The precision of the discretization method used in spatial directions is twice the order of the corresponding fractional derivatives. It is proved that the proposed method is unconditionally stable via the matrix analysis method and the maximum error in achieving convergence is discussed. Numerical example is considered aiming to demonstrate the validity and applicability of the proposed technique.

In this paper, we present a two-step Ulm-type method to solve systems of nonlinear equations without computing Jacobian matrices and solving Jacobian equations. we prove that the two-step Ulm-type method converges locally to the solution with R-convergence rate 3. Numerical implementations demonstrate the effectiveness of the new method.

{P1,P2}-Nekrasov matrices represent a generalization of Nekrasov matrices via permutations. In this paper, we obtained an error bound for linear complementarity problems for fP1; P2g-Nekrasov matrices. Numerical examples are given to illustrate that new error bound can give tighter results compared to already known bounds when applied to Nekrasov matrices. Also, we presented new max-norm bounds for the inverse of {P1,P2}-Nekrasov matrices in the block case, considering two different types of block generalizations. Numerical examples show that new norm bounds for the block case can give tighter results compared to already known bounds for the point-wise case.

In this paper, we present a numerical method for solving nonlinear Hammerstein fractional integral equations. The method approximates the solution by Picard iteration together with a numerical integration designed for weakly singular integrals. Error analysis of the proposed method is also investigated. Numerical examples approve its efficiency in terms of accuracy and computational cost.

In this paper we study some new dynamic Steffensen-type inequalities on a general time scale. More precisely, we deal with time scale spaces with positive ?-finite measures. As an application, our results are compared with some previous results known from the literature. It turns out that our results generalize some previously known Steffensen-type inequalities in a classical setting.

Recently, a typical neural dynamics called Zhang dynamics (ZD) has been developed for online solution of dynamic linear matrix-vector inequality. This paper show a summary result by presenting the discrete-time forms of such a ZD for dynamic linear matrix-vector inequality solving. Specifically, by exploiting four different kinds of Taylor-type difference rules, the resultant discrete-time ZD (DTZD) algorithms, which are called respectively the DTZD-I, DTZD-II, DTZD-III, and DTZD-IV algorithms, are established. These algorithms can achieve excellent computational performance in solving dynamic linear matrix-vector inequality. The theoretical and numerical results are presented to further substantiate the efficacy of the presented four DTZD algorithms.

In this paper, we propose the first hyperbolic-logarithmic kernel function for Semidefinite programming problems. By simple analysis tools, several properties of this kernel function are used to compute the total number of iterations. We show that the worst-case iteration complexity of our algorithm for large-update methods improves the obtained iteration bounds based on hyperbolic [24] as well as classic kernel functions. For small-update methods, we derive the best known iteration bound.

In the present paper, we introduce and study (A,?) -statistical convergence of order ?, using the ?-function, infinite matrix and we establish some inclusion theorems.

Mittag-Leffer function is very useful in the theory of fractional differential equations. Ostrowski?s inequality is very important in numerical computations and error analysis of numerical quadrature rules. In this paper, Ostrowski?s inequality via generalized Mittag-Leffer function is established. In application point of view, bounds of fractional Hadamard?s inequalities are straightforward consequences of these inequalities. The presented results are also contained in particular several fractional inequalities and have connection with some known and already published results.

Due to their applications in many branches of science, topological graph indices are becoming more popular every day. Especially as one can model chemical molecules by graphs to obtain valuable information about the molecules using solely mathematical calculations on the graph. The inverse problem for topological graph indices is a recent problem proposed by Gutman and is about the existence of a graph having its index value equal to a given non-negative integer. In this paper, the inverse problem for Bell index which is one of the irregularity indices is solved. Also a recently defined graph invariant called omega invariant is used to obtain several properties related to the Bell index.

Compared to the linear activation function, a suitable nonlinear activation function can accelerate the convergence speed. Based on this finding, we propose two modified Zhang neural network (ZNN) models using different nonlinear activation functions to tackle the complex-valued systems of linear equation (CVSLE) problems in this paper. To fulfill this goal, we first propose a novel neural network called NRNN-SBP model by introducing the sign-bi-power activation function. Then, we propose another novel neural network called NRNN-IRN model by introducing the tunable activation function. Finally, simulative results demonstrate that the convergence speed of NRNN-SBP and the NRNN-IRN is faster than that of the FTRNN model. On the other hand, these results also reveal that different nonlinear activation function will have a different effect on the convergence rate for different CVSLE problems.

By introducing the real inner product, this paper offers an modified conjugate gradient least squares iterative algorithm (MCGLS)for solving the generalized Sylvester-conjugate matrix equation. The properties of this algorithm are discussed and the finite convergence of this algorithm is proven. This new iterative method can obtain the symmetric least squares Frobenius norm solution within finite iteration steps in the absence of roundoff errors. Finally, two numerical examples are offered to illustrate the effectiveness of the proposed algorithm.

In this paper, the author introduces parabolic generalized local Morrey spaces and parabolic local Campanato spaces, respectively and also establishes parabolic local Campanato estimates for commutators of parabolic fractional maximal and integral operators with rough kernel on parabolic generalized local Morrey spaces.

Aiming at the nonlinear convection diffusion equation with the numerical oscillations, a numerical stability algorithm is constructed. The basic principle of the finite point algorithm is given and the computational scheme of the nonlinear convection diffusion equation is deduced. Then, the numerical simulation of the one-dimensional and two-dimensional nonlinear convection-dominated diffusion equation is carried out. The relationship between the calculation result and the support domain size, step size and time is discussed. The results show that the algorithm has the characteristics of simplicity, stability and efficiency. Compared with the traditional finite element method and finite difference method, the new algorithm can attain a higher calculation accuracy. Simultaneously, it proves that the method given in this paper is effective to solve the nonlinear flow diffusion equation and can eliminate the numerical oscillations.