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This paper deals with a generalized multidirectional associative memory neural network with time-varying coefficients and mixed delays. Some criteria are established for the existence and the global exponential stability of weighted pseudo almost-periodic solutions for the studied model. To do so, the exponential dichotomy theory, the contraction mapping fixed point theorem and the differential inequality techniques are used. Moreover, an example and its numerical simulation are employed to illustrate the main results.

In this paper, an iterative method for multiple roots of nonlinear equations is presented. Its convergence order is analyzed and proved. It is shown that the proposed method has third-order convergence. To assess the validity and performance of the proposed method, some nonlinear equations are solved and the results are compared with the results from six other methods.

In this paper, we introduce a combination of family of some conjugate gradient methods (CG) with the trust-region method. Whenever the trust-region algorithm is unsuccessful, a family of CG methods is used to prevent resolving the trust-region subproblem. The computational cost for such a family is trivial. The global theory of the new approach is proved and numerical experiments are reported.

In this paper, we prove some fixed point theorems by introducing a new F-contraction namely $$S_F$$ -contraction in fuzzy metric spaces by combining the idea of Wardowski’s (Fixed Point Theory Appl 2012, Article ID 94, 2012) and Secelean’s (Fixed Point Theory Appl 2013, Article ID 277, 2013) contractions in metric spaces and Grabiec’s (Fuzzy Sets Syst 125, 385–389, 1988) contraction in fuzzy metric spaces. An example is also given to support the results proved herein.

The aim of this paper is to give the predictable representation property associated with Levy process in the non-homogeneous case. In this latter, we establish the existence and uniqueness of solution for the Backward Stochastic Differential Equations and its relation with Partial integro-differential equations.

The purpose of this paper is to present some characterizations of almost fuzzy prime ideals and sub modules; and to introduce certain innovative fuzzy prime ideals and sub modules respectively. Moreover, every fuzzy ideal in R is an almost prime ideal for a quasi-local ring \( (R, M) \) with \( M^{2} = 0 \). Moreover, prime sub module µN in a finitely generated multiplication R − module M and fuzzy prime ideal \( I_{\mu } \) in R have been constructed.

In this paper, some iterative methods with third order convergence for solving the nonlinear equation were reviewed and analyzed. The purpose is to find the best iteration schemes that have been formulated thus far. Hence, some numerical experiments and basin of attractions were performed and presented graphically. Based on the five test functions it was found that the best method is D87a due Dong’s Family method (Int J Comput Math 21:363–367, 1987).

In this paper we prove the existence of mild solutions for a second-order impulsive semilinear stochastic differential inclusion with a standard cylindrical Wiener process and Poisson jumps. We consider the case in which the right hand side can be either convex-valued.

The warped product $$M_1 \times _F M_2$$ of two Riemannian manifolds $$(M_1,g_1)$$ and $$(M_2,g_2)$$ is the product manifold $$M_1 \times M_2$$ equipped with the warped product metric $$g=g_1 + F^2 g_2$$ , where F is a positive function on $$M_1$$ . The notion of warped product manifolds is one of the most fruitful generalizations of Riemannian products. Such a notion plays very important roles in differential geometry as well as in physics, especially in general relativity. In this paper we study warped product manifolds endowed with a Tripathi connection. We establish some relationships between the Tripathi connection of the warped product M to those $$M_1$$ and $$M_2$$ .

In the present paper, we investigate the commutativity of 3-prime near-rings satisfying certain conditions involving left generalized multiplicative derivations on semigroup ideals. Moreover, examples have been provided to justify the necessity of 3-primeness condition in the hypotheses of various results.

For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nystrom and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree $$\le r - 1.$$ We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4r in the interpolation at Gauss points can be improved to $$4r+2$$ . We illustrate the improvement of the order of convergence by numerical experiments.

In this paper, we extend the $$\beta $$ -Weil pairing, initially introduced in the setting of ordinary elliptic curves with even embedding degree by Aranha et al. [2], to ordinary elliptic curves of any embedding degree. We also propose a new optimal pairing which is the product of some rational functions with the same Miller loop and having a simple final exponentiation. The new pairing is appropriated for using the multi-pairing technique for an efficient implementation. We focus our computation at high security level. Exploiting the fact that the $$\beta $$ -Weil pairing is suitable for parallel execution, we first show that calculating the extended $$\beta $$ -Weil pairing over pairing-friendly elliptic curves with embedding degree 27 is more efficient than calculating the optimal ate pairing. Finally we show that calculating our new pairing over Barreto–Lynn–Scott curves with embedding degree 12 (BLS12) and pairing-friendly elliptic curves with embedding degree 15 is more efficient than calculating the optimal ate pairing.

In this paper we aims to obtain new exact and analytical solutions for extended Korteweg–de Vries (K–dV) equation by using of new modified method named Riccati equation method. We introduce the extended K–dV equation with help of the reductive perturbation method, which admits a double layer structure in current plasma model. The obtained solutions are expressed by the hyperbolic, trigonometric and rational functions. Our calculations show that, considered method is straightforward to solve nonlinear partial differential equations. This method is not only powerful mathematical tool for generating more solutions of nonlinear partial differential equations but also can be applied to nonlinear partial differential equations.

The objective of this paper is to introduce and study some sequence spaces over the geometric complex numbers by means of Museilak–Orlicz function. We make an effort to study some topological properties and inclusion relations between these sequence spaces. Moreover, by using the concept of non-Newtonian calculus we prove the completeness of the spaces.

In this paper we study the decomposition structure of a direct image of a polynomial ring under certain map.

S. Ramanujan has recorded many theta-function identities in his notebooks and ‘Lost’ notebook. Inspired by the works of Ramanujan, recently M. Somos discovered several new theta-function identities using PARI/GP scripts without offering the proof, which are analogous to Ramanujan’s theta-function identities. In this paper, we give proofs for some theta-function identities of level 8 discovered by Somos. Furthermore, we extract some partition identities from them.

In the paper we study the uniqueness problem of certain differential polynomials generated by two meromorphic functions provided they share a small function along with some other conditions on the zeros and poles of the concerned functions.

In the present paper, we determine necessary and sufficient conditions for zF(a, b; c; z) and $$z(2-F(a,b;c;z))$$ where $$F(a,b;c;z)=\sum \nolimits _{n=0}^{\infty }[(a)_{n}(b)_{n}/(c)_{n}(1)_{n}]z^{n}$$ to be in a certain class of analytic functions with negative coefficients. Furthermore, we consider an integral operator related to hypergeometric functions.

In this paper, we define some new number sequences, which we represent as $$ (B_{n}),(b_{n}),(y_{n})$$ and present relations of these new sequences with each other. Then, we give all positive integer solutions of some Diophantine equations in terms of these new sequences.

In the present paper, we study the existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator (p, q)-Laplacian with indefinite weights at resonance cases.

In this paper, we introduce Halpern-type proximal point algorithm for approximating a common solution of monotone inclusion problem and fixed point problem. We obtain a strong convergence of the proposed algorithm to a common solution of finite family of monotone inclusion problem and fixed point problem for nonexpansive mappings in complete CAT(0) spaces. Nontrivial application and numerical example were given. Our results complement and extend some recent results in literature.

In this paper, we are mainly interested to find the sufficient conditions on parameters A, B, b and c that will ensure the generalized Struve function $$ u_{v,b,c}$$ satisfies the subordination $$u_{v,b,c}\left( z\right) \prec \left( 1+Az\right) /\left( 1+Bz\right) $$ .

In this paper, we introduce and investigate the subclasses $$\mathcal {Q} _{g}^{\zeta }(m,\lambda ,\mu ;\gamma )$$ and $$\mathcal {H}_{g}^{\zeta }(m,\lambda ,\mu ,r;u)$$ of analytic functions of complex order defined by a new differential operator involving binomial series. Furthermore, We obtain coefficients bounds and coefficient estimates involving of the nonhomogeneous Cauchy–Euler differential equation of order r. Several corollaries of the main results are also considered.

In this paper we study the existence, stability and smoothness of bounded solutions for an impulsive semilinear system of parabolic equations with homogeneous Dirichlet boundary condition. Using Banch fixed point theorem, we prove the existence of bounded solutions assuming that the nonlinear terms satisfy a Lipschitz condition, after that, we study the stability and the smoothness of such solutions.

In this paper, some fundamental relationships of a $$\Gamma $$ -semihypergroup and its operator semihypergroup in terms of fuzzy subsets, fuzzy hyperideals and fuzzy hyperideal extension are obtained. Using these in obtaining some characterization theorems of $$\Gamma $$ -semihypergroups in terms of fuzzy subsets, we highlight the effectiveness of operator semihypergroups in the study of $$\Gamma $$ -semihypergroups in terms of fuzzy subsets.

This paper summarizes the contents of a plenary talk at the Pan African Congress of Mathematics held in Rabat in July 2017. We provide a survey of recent results on spectral properties of Schrodinger operators with singular interactions supported by manifolds of codimension one and of Robin billiards with the focus on the geometrically induced discrete spectrum and its asymptotic expansions in term of the model parameters.

In this paper, we study the stability of some essential B-spectra of closed linear operators on a Banach space X, under polynomially finite rank operators and we give the characterization of some essential B-spectra of a $$2\times 2$$ of unbounded matrix operator acting in the product of Banach spaces $$X\times Y$$ . Then, using the functional calculus, we prove that a spectral mapping type theorem holds for these essential B-spectra. As an application, we study the effect of the functional calculus on the class of meromorphic operators, and on the class of isoloid operators with sable sign index, satisfying generalized Weyl theorem.

The purpose of this paper is to introduce a strongly convergent algorithm for minimizingthe distance function under the solution set of a split equilibrium problem involvingpseudomonotone bifunctions. The proposed algorithm can be considered as a combination of the extragradient method for pseudomonotone equilibrium problems and a projectionprocedure for convex optimization. Under the commonly used assumptions inpseudomonotone equilibrium problems, the iterations generated by the algorithm are proved to converge strongly to the unique solution of the considered problem. We then apply the algorithm to a jointly constrained Nash equilibrium model. A simple numerical example is given to illustrate the proposed algorithm.

An ai-semiring is a semiring S such that $$a+a=a$$ for all $$a \in S$$ . In the present paper, we characterize minimal k-bi-ideals and minimal strong quasi k-ideals in ai-semirings. We show that every minimal k-bi-ideal is a product of a minimal right k-ideal and a minimal left k-ideal of S, and conversely. Also we prove a number of equivalent characterizations for a k-bi-ideal to be minimal. Minimal strong quasi k-ideals are precisely intersections of a minimal left k-ideal and a minimal right k-ideal of S. As a consequence, we show that a strong quasi k-ideal is minimal if and only if it is an $${\mathcal {{\overline{H}}}}$$ -class.

The collision between a 3-Dimensional randomly moving meteor with the satellite is studied from a probability point of view. The satellite moves along slinky-turn-ellipse curve and starts its motion from a known point $$ (X_{0} ,Y_{0} ,Z_{0} ) $$ . The meteor comes from a distant space with dynamic random movement. The main contribution of this paper is to find the conditions that make the expected value of the collision time is finite. In addition, we obtain two candidate utility functions namely the mean time to collision and the cumulative probability of collision. Also, we obtain the estimated distance between them at any time $$ t $$ by using Bayes estimation method. An example with numerical results is given to show the effectiveness of this method.

In this paper it is constructed a new Besov–Morrey type spaces. Utilizing integral representation of generalized derivatives of functions defined on n-dimensional domains satisfying flexible $$\varphi $$ -horn condition an embedding theorem is proved. Also, it is proved that the generalized derivatives of functions from this spaces satisfies the generalized Holder condition.

In this paper, we consider the concept of b-generalized pseudodistances with the concept of weak contraction for non-self mapping by provide the condition guarantee the existence of best proximity point and an algorithm for determining such an optimal approximate solution to the problem of globally minimizing the error $$\inf \{ d(x,y): x \in A,y\in B\}$$ where A and B are nonempty close subsets of b-metric spaces X. Also, we give some example to illustrate our main result.

In this paper, an efficient numerical method is proposed for solving a nonlinear system of Volterra–Fredholm integral equations of the second kind, using two-dimensional radial basis functions (RBFs). This method is based on interpolation by radial basis functions including multiquadric (MQ), using Legendre–Gauss–Radau nodes and weights. The proposed method does not require any background mesh or cell structures, so it is meshless and consequently independent of the geometry of domain. Newton method is employed for solving the nonlinear system obtained with MQ RBF collocation method. Also a theorem is proved for convergence analysis. Some numerical examples are presented and the results are compared with the analytical solution to demonstrate the validity and the applicability of the proposed method.

In this paper, we describe multiplication and weighted composition operators induced by functions which either are strongly $$\mu $$ -normable measurable or have strong $$\mu $$ -measurability of the orbits on Lorentz–Karamata–Bochner (LKB) spaces $$L_{p,q;b}$$ , where $$1< p \le \infty $$ , $$1\le q \le \infty $$ and b is a slowly varying function.

The objective of the present paper is to study results that are defined using the notions of generalization of Janowski classes and k-symmetrical functions. A representation theorem, coefficients inequality, distortion properties and the result on radius of starlikeness are discussed.

In this paper, we show that the generalized prolate spheroidal wave functions (GPSWFs), called sometimes Slepian’s functions, can be defined as the most concentrated functions among functions in some reproducing kernel Hilbert spaces (RKHS for short). As a consequence, we use them the GPSWFs to approximate the sets of K-bandlimited functions that are essentially time limited to an interval (a, b).

This paper is devoted to introduce the notions of n-fold left-(right-)Heyting, n-fold left-(right-)Boolean and n-fold left-(right-)MV filters in residuated lattices and to investigate their properties. Several characterizations of these notions are derived. The relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)Heyting filters are investigated and we prove that an n-fold left-(right-)Boolean filter is an n-fold left-(right-)Heyting filter, respectively, and this implication is strict. Also, the relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)MV filters are investigated and we show that a normal n-fold left-(right-)Boolean filter is a normal n-fold left-(right-)MV filter and each n-fold left-(right-)Heyting and n-fold left-(right-)MV filter is an n-fold left-(right-)Boolean filter.

In this paper, we investigate asymptotic stability of solutions of some nonlinear vector differential equations of third order with delay. Our results include and improve some well-known results in the literature.

This paper studies relationship between bipolar fuzzy sets, rough sets and $$\Gamma $$ -semihypergroups. We study the notion of rough bipolar fuzzy $$\Gamma $$ -hyperideals in $$\Gamma $$ -semihypergroups. Then we prove that the lower and upper approximation of a bipolar fuzzy $$\Gamma $$ -hyperideal is a bipolar fuzzy $$\Gamma $$ -hyperideal.

The present paper deals with a harvested predator–prey model and the dynamics of tourists in wetlands. This model describes the coexistence and extinction of at least one of the species in the wetlands. By the Mahwin continuation theorem of coincidence degree theory, we prove the existence of a positive periodic solution (in place of an equilibrium) provided that the harvest rate of prey is in a suitable range. Further, by constructing a suitable Lyapunov functional, we obtain sufficient conditions for global asymptotic stability of the positive periodic solution. Finally numerical simulations are carried out to illustrate the feasibility of the mathematical results.

In this paper, by making use of the principle of subordination, we investigate some subordination and convolution properties of certain subclasses of $$\ p$$ -valent analytic functions which are defined by the Srivastava–Saigo–Owa fractional differintegral operator.

In this paper, we introduce certain new subclasses of the bi-univalent function class $$\sigma $$ in which both f and $$f^{-1}$$ are m-fold symmetric analytic with their derivatives in the class $${\mathcal {P}}$$ of analytic functions. Furthermore, we obtain coefficient bounds of $$|a_{m+1}|$$ and $$|a_{2m+1}|$$ for these new subclasses.

In this paper, we obtain the estimates with k-th root transformation for certain classes of analytic univalent functions using quasi-subordination. Some interesting remarks of the results presented here are also discussed.

In this paper, soft int-groups, soft normal int-groups and their basic properties are presented. Normal soft int-subgroup of a soft int-group is defined and relations concerning them are given. Then, homomorphism and isomorphism theorems are applied to the soft int-groups.

It is a well known fact that there exist irreducible polynomials P(X) over \(\mathbb {Z}\) that are not p-Eisenstanian for any prime number p at a first glance but, after a linear transformation Eisenstein criterion could be applied to obtain their irreducibility. One of the main purpose of this paper is to give families of irreducible quartics that are not of this kind. We also study the problem of the root separation for quartic polynomials.

In this paper, the fourth order ordinary differential equation (ODE) of the form $$y^{(iv)}=f(x,y,y',y'',y''')$$ subject to initial or boundary conditions is solved directly without reducing the higher ODE into an equivalent first order system. This is accomplished by constructing a continuous fifth derivative method (CFIDM) which is used to produce the main and additional discrete fifth derivative methods (FIDMs). The FIDMs are then assembled and applied as a single block matrix equation to simultaneously provide all approximations on the entire interval of interest for the initial or boundary value problem. The convergence analysis of the method is discussed. The accuracy of the method is illustrated via numerical experiments.

The purpose of this paper is to introduce subclasses of multivalent functions by using Srivastava–Saigo–Owa fractional differintegral operator and investigate various properties for these subclasses. Also, we investigate inclusion relations involving the operator $$F_{p,c}$$ .

In this paper we investigate the n-iterated exponent of convergence of $$ f^{\left( i\right) }-\varphi $$ where $$f\not \equiv 0$$ is a solution of linear differential equation with analytic and meromorphic coefficients in the unit disc and $$\varphi $$ is a small function of f. By this investigation we can deduce the value distribution of the fixed points of $$f^{\left( i\right) }$$ by taking $$\varphi \left( z\right) =z$$ . This work is an extension to the unit disc and an improvement of recent results in the complex plane by Xu et al. (Adv Differ Equ 2012(114):1–16, 2012) and Tu et al. (Adv Differ Equ 2013(71):1–16, 2013).

In this paper, we consider the Laplacian energy of digraphs. Various approaches for the Laplacian energy of a digraph have been put forward by different authors. We consider the skew Laplacian energy of a digraph as given in Cai et al. (Trans Combin 2:27–37, 2013). We obtain some upper and lower bounds for the skew Laplacian energy which are better than some previous known bounds. We also show every even positive integer is the skew Laplacian energy of some digraphs.

Several authors have studied the growth properties of Dirichlet series and vector valued Dirichlet series (VVDS). Wen Ping Huang, Ju Hong Ning and Jin Tu have obtained various results by considering Dirichlet series with complex exponents. In this paper we obtainthe characterizations of order and type of vector valued Dirichlet series which generalize some well known results for growth of classical Dirichlet series. Further we have tried to study the growth properties of holomorphic vector valued Dirichlet series with complex exponents.