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In the paper, starting from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds, by virtue of the Faà di Bruno formula, with the help of two identities for the Bell polynomials of the second kind, and making use of a new inversion theorem for combinatorial coefficients, the authors derive two nice explicit formulas and their corresponding inversion formulas for the Chebyshev polynomials of the first and second kinds. [ABSTRACT FROM AUTHOR]

The Szeged index is a modification of the Wiener index to cyclic molecules. The Szeged index of a connected graph G is defined as SZ(G)= Σe∈E(G) n1(e|G)n2(e|G), where E(G) is the edge set of G, and for any e = uν ∈ E(G), n1(e|G) is the number of vertices of G lying closer to vertex u than to vertex ν, and n2(e|G) is the number of vertices of G lying closer to vertex ν than to vertex u. In this paper, we determine the n-vertex unicyclic graphs whose vertices on the unique cycle have degree at least three with the first, the second and the third smallest as well as largest Szeged indices for n ≥ 6, n ≥ 7 and n ≥ 8, respectively. [ABSTRACT FROM AUTHOR]

In this paper we study some properties of the solutions of a second order system of functional-differential equations with maxima, of mixed type, with "boundary" conditions. We use the weakly Picard operator technique. [ABSTRACT FROM AUTHOR]

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant φ-sectional curvature, and prove the structure theorem for ξ-conformally flat and φ-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an η-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature ε. [ABSTRACT FROM AUTHOR]

The paper is about investigating the uniform convergence conditions of spectral expansions of continuous functions in terms of root functions of a spectral problem with the same eigenparameter in the second-order differential equation and depending on quadratically in one of the boundary conditions on a closed interval. [ABSTRACT FROM AUTHOR]

Hybrid numbers generalize complex, hyperbolic and dual numbers, simultaneously. Special kinds of hybrid numbers, related to numbers of Fibonacci type, among others Pell numbers, were introduced quite recently. In this paper we introduce and study polynomials, which are a generalization of Pell hybrid numbers and so called Pell hybrinomials. [ABSTRACT FROM AUTHOR]

In this paper, we present new kinds of reciprocal sums of finite products of general second order linear recurrences. In order to evaluate explicitly them by q-calculus, first we convert them into their q-notation and then use the methods of partial fraction decomposition and creative telescoping. [ABSTRACT FROM AUTHOR]

In this paper we study functional-differential equations on the semi-axis, which are non-linear with respect to the phase variables and linear with respect to the control. Sufficient conditions for existence of optimal control in terms of the right-hand side and the quality criterion are obtained. Relation between the solutions of the problems on infinite and finite intervals is studied and results that about these connections are proven. [ABSTRACT FROM AUTHOR]

In this paper, we introduce four new iterative schemes by modifying the shrinking projection method with Ishikawa iteration and S-iteration. The strong convergence theorems are given for obtaining a common fixed point of two G-nonexpansive mappings in a Hilbert space with a directed graph. We also give some numerical experiments for supporting our main theorems and compare convergence rate between them. [ABSTRACT FROM AUTHOR]

In this paper, the approximate solutions by using the undetermined fuzzy coefficients method and the exact solutions by using the Hukuhara differentiability of second-order fuzzy linear boundary value problems with constant coefficients are investigated. Thus, comparisons of the found solutions are given. [ABSTRACT FROM AUTHOR]

In this paper we introduce the generalized bi-periodic Fibonacci and Lucas quaternions which are the further generalizations of the bi-periodic Fibonacci and Lucas quaternions considered in the literature. For those quaternions, we derive the generating functions, Binet's formulas and Catalan's identities. [ABSTRACT FROM AUTHOR]

The intended objective of this paper is to introduce a new class of polynomials, namely the extended Laguerre-Gould-Hopper-Sheffer polynomials. The generating function and operational rule are derived by making use of integral transform. Their quasi-monomial properties and determinant forms are also established. Examples of certain members belonging to the extended Laguerre-Gould-Hopper-Sheffer polynomials are constructed and their corresponding results are established. [ABSTRACT FROM AUTHOR]

In this paper, the author considers the one dimensional initial-boundary problem for a pseudo-parabolic equation with time delay in second spatial derivative. To solve this problem numerically, the author constructs higher order difference method and obtain the error estimate for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Some numerical examples illustrate the convergence and effectiveness of the numerical method. [ABSTRACT FROM AUTHOR]

In this work we solve in closed form the system of difference equations xn+1=aynxn-1+bxn-1+c/ynxn-1; yn+1 = axnyn-1+byn-1+c/xnyn-1; n=0,1,..., where the initial values x-1, x0, y-1 and y0 are arbitrary nonzero real numbers and the parameters a, b and c are arbitrary real numbers with c ≠ 0. In particular we represent the solutions of some particular cases of this system in terms of Tribonacci and Padovan numbers and we prove the global stability of the corresponding positive equilibrium points. The results obtained here extend those obtained in some recent papers. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is twofold: on the one hand to set up an axiomatic system defining an order-embedding between infinite σ-algebras to generalize the powering mapping and investigate some additional necessary and sufficient condition for the postulate of powering to hold in the system, and on the other hand to provide some theoretical applications. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

This paper is concerned with a Shimizu-Morioka model with constant delays. Its stability of the equilibrium is investigated and the existence of Hopf bifurcations is demonstrated by analyzing the associated characteristic equation. Furthermore, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the center manifold theory and the normal form method. Finally, special attention is paid to numerical simulations in order to verify the theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, using the Mellin transform of Airy function we present an integral addition formula for the function ... In deriving this representation, we make use of the Hankel functions of first kind and apply this representation to get the Green function of triharmonic heat equation in terms of the Airy functions. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the convergence of the fitted mesh method applied to singularly perturbed Volterra delay-integro-differential equation. Our mesh comprises a special nonuniform mesh on the first subinterval and uniform mesh on another part. Error estimates are obtained using difference analogue of Gronwall's inequality with delay. A numerical test that confirms the theoretical results is presented. [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete population model and obtain a couple of criteria to guarantee our model being stable, including the global attractor, the extreme stability, and the periodicity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new generalized inverses of matrices, namely, the hi;mi-core inverse and the (j, m)-core inverse. The (i, m)-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalary and Trenkler [1] and the core-EP inverse defined by Manjunatha Prasad and Mohana [10]. The (j, m)-core inverse of a complex matrix extends the notions of the core inverse and the DMP-inverse defined by Malik and Thome [9]. Moreover, the formulae and properties of these two new concepts are investigated by using matrix decompositions and matrix powers. [ABSTRACT FROM AUTHOR]

In this paper certain invariants of conformal mappings of the generalized Riemannian space are obtained. Here are the general results. These invariants are the analogues of the Thomas projective parameter and generalized Weyl projective tensor. [ABSTRACT FROM AUTHOR]

In this paper,we study the existence and multiplicity of solutions for a perturbed three-point boundary value problem of Kirchhoff-type. The approach is based on variational methods and critical point theory.As applications of these methods,we get several multiplicity results for the problems under consideration. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials Fnk (x, s, q) and the incomplete q-Lucas polynomials Lnk (x, s, q), respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the (p, q)-analogues (with 0 < q < p ≥ 1) by applying some obvious parametric variations, the additional parameter p being redundant. [ABSTRACT FROM AUTHOR]

In the paper, by methods and techniques in combinatorial analysis and the theory of special functions, the authors discuss two kinds of special values for the Bell polynomials of the second kind for two special sequences, find a relation between these two kinds of special values for the Bell polynomials of the second kind, and derive an identity involving the combinatorial numbers. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the umbral representation of the geometric polynomials wxn; = wn (x) to derive some properties involving these polynomials. Furthermore, for any prime number p and any polynomial f with integer coefficients, we show (f (wx))p≡ f (wx) (mod p) and we give other curious congruences. [ABSTRACT FROM AUTHOR]

In the first part of this work we present some basics about the connection of exponential dichotomy and Floquet-theory. Then we study some stability notions of linear differential equations based on the concept of the exponential and ordinary dichotomy. More precisely we shall show that the definition of the asymptotical (Lyapunov-) stability can be formulated by using the exponential dichotomy. In the main part of the paper we consider parameter dependent non-autonomous linear and autonomous nonlinear systems which have at a certain value of the parameter an asymptotically stable solution. Then we examine the question how much the parameter can be changed such that the solution remains asymptotically stable. Finally, we study the orbital stability of periodic solutions of autonomous systems applying the previous results. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we study Δ-convergence and strong convergence of the sequence generated by the extragradient method for pseudo-monotone equilibrium problems in Hadamard spaces. We first show Δ-convergence of the generated sequence to a solution of the equilibrium problem, then the strong convergence of Halpern regularization method is proved. Finally we give some examples where the main results can be applied. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with 2p-order Hamiltonian systems with impulsive effects. We investigate the variational structure associated to this system. In addition, we obtain some results of multiple solutions for asymptotically linear 2p-order Hamiltonian systems via variational methods and critical point theorems. Meanwhile, some examples are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we shall derive formulæ for partial sums of the Gaussian q-binomial coefficients, their reciprocals, squares and squared reciprocals. To prove the claimed results, we use q-calculus. As applications of our results, we give some interesting generalized Fibonomial sums formulæ. [ABSTRACT FROM AUTHOR]

In this paper we discuss some convergence and divergence properties of subsequences of logarithmic means of Walsh-Fourier series. We give necessary and sufficient conditions for the convergence regarding logarithmic variation of numbers. [ABSTRACT FROM AUTHOR]

The topic of rough set theory considers a relation to determine the lower and upper approximations of a set X. Originally, this relation was assumed to be an equivalence relation. This research focuses on using tolerance relations instead of equivalences, i.e. we do not assume the transitivity of the relations. More specifically, in this paper we investigate tolerances induced by irredundant coverings. We characterize the interrelation between the lattices of lower and upper approximations of such tolerances R and p. The theory of Formal Concept Analysis makes it possible to examine the inclusions of the resulting concepts. We also use quasiorders (denoted by ≤ and ≥ (p)) and an equivalence relation (denoted by ker p) for summarizing the connection between tolerances and lattices in a theorem. [ABSTRACT FROM AUTHOR]

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself is equal to a given element of the ring. [ABSTRACT FROM AUTHOR]

In this paper, Seiberg Witten like equations are constructed on 7 manifolds endowed with G2-structure, lifted by SU(3)-structure. Then a global solution is obtained on the strictly-Pseudoconvex CR 7-manifolds for a given negative and constant scalar curvature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the operator ... on the sequence space c0 where the non-zero diagonals are the entries of an oscillatory sequence. [ABSTRACT FROM AUTHOR]

We consider the following second order impulsive differential equation with delays ... In this paper we obtain sufficient conditions of nonpositivity of Green's functions for impulsive differential equation. All results are formulated in the form of theorems about differential inequalities. It should be noted that the sign-constancy of the coefficients bj (t) was assumed in all the literature devoted to impulsive functional differential equations. One of the main purposes of this work is to propose a technique allowing us to avoid these assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

In this paper, we extend relation-theoretic contraction principle due to Alam and Im- dad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T -transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702), Agarwal et al: (Applicable Analysis, 87 (1) (2008) 109-116), Berzig and Karapinar (Fixed Point Theory Appl. 2013:205 (2013) 18 pp), Berzig et al: (Abstr. Appl. Anal. 2014:259768 (2014) 12 pp) and Turinici (The Sci. World J. 2014:169358 (2014) 10 pp). [ABSTRACT FROM AUTHOR]

In this paper, the second regularized trace formula for the differential operator with antiperiodic boundary conditions is obtained. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce two new classes of multifunctions called almost δ-semicontinuous multifunctions and weakly δ-semicontinuous multifunctions which are generalization of δ-semicontinuous multifunctions. In this paper we obtain several properties of such multifunctions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new look at Finsler surfaces. Landsberg surfaces are Finsler surfaces that are solutions of a system of non-linear partial differential equations. Considering the unicorn’s Landsberg problem, we reduce this system to a single non-linear PDE which we call the Landsberg’s PDE. By making use of the new look of Finsler surfaces, we solve the Landsberg’s PDE and get a class of solutions. Moreover, we show that these solutions and their conformal transformations are Berwaldain.

In this paper, we introduce the concept of the statistical convergence with respect to solid topology and Riesz valued norms on lattice-normed locally solid Riesz spaces. Moreover, we give the notions of statistically pτpτpτpτ

In the present paper, we give the bounds for the second Hankel determinant of the logarithmic coefficients of a certain subclass of normalized univalent functions, which we have introduced here. Relevant connections of the results, which we have presented here, with those available in the existing literature are also described briefly.

This paper introduces self maps satisfying (CLRα)(CLRαβ)

In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point theorem. Simple examples follow the main results in successive sections.

In this paper, we prove the boundedness of the Riesz potential Iα

The paper aims to present a new primary ideal in a commutative ring Rn1n1n1

In this paper, we study the character values of homogeneous monotonic P-polynomial table algebras with finite dimension d≥5z

In this paper, we establish some new existence results for certain coupled systems of nonlinear Ψ

The Legendre wavelet based method has been employed in this paper to investigate neutral delay differential equations. The highest order derivative is approximated by Legendre wavelet using the integral operator technique. Then integrations of Legendre wavelet are used to approximate the lower order derivatives and unknown function. To get an algebraic system of linear or nonlinear equations, approximated values of unknown function and its derivatives are substituted in neutral delay differential equations. On solving the developed system, we get unknown wavelet coefficients and subsequently the approximate solution. To analyze the theoretical usability of the approach, the upper bound of error norm is established. Moreover, the theoretical results are confirmed through few numerical experiments. A comparison of the results of presented method with method available in literature is given to conclude the superiority of the proposed method.