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In this paper, a new type of stability for nonlinear systems of differential equations called practical ψγ-exponential asymptotic stability, is presented. Some sufficient conditions for practical ψγ-exponential asymptotic stability are provided by using Lyapunov theory. These results generalize fundamental well known results for practical exponential asymptotic and ψ-exponential asymptotic stability for nonlinear time-varying systems. In addition, these results are using to investigate the practical ψγ-exponential asymptotic stability problem of nonlinear perturbed system and cascade systems. The last part is devoted to the study the problem of practical ψγ-exponential asymptotic stabilization for some classes of nonlinear systems with delayed perturbation. [ABSTRACT FROM AUTHOR]

In this paper we investigate the almost everywhere convergence of two dimensional Marcinkiewicz-like means of two variable integrable functions which is given by... (M|n| ≤ n

In this paper, half inverse spectral problem for diffusion operator with jump conditions dependent on the spectral parameter and discontinuity coefficient is considered. The half inverse problems is studied of determining the coefficient and two potential functions of the boundary value problem its spectrum by Hocstadt-Lieberman and Yang-Zettl methods. We show that two potential functions on the whole interval and the parameters in the boundary and jump conditions can be determined from the spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we establish interesting sums including generalized harmonic numbers and special numbers by using generating functions of these numbers and some combinatorial identities. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of fuzzy barrels on locally convex fuzzy topological vector spaces. We present some characterizations of the fuzzy locally convex spaces, which are fuzzy barrelled. Using fuzzy barrels, we prove that the same fuzzy sets are bounded in any fuzzy topology of dual pair. Finally, we prove the Banach-Steinhaus theorem for the fuzzy topological vector spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear impulsive differential equation system with piecewise constant mixed arguments and prove the existence and uniqueness of a solution. Moreover, we obtain sufficient conditions for oscillation of the solution and give an example for it. Finally, we show that the solution of the modified version of this equation is k periodic. [ABSTRACT FROM AUTHOR]

Results reported in this paper provide a generalization for some previously obtained results. Based on comparing with the oscillatory behavior of first-order delay equations, we provide new oscillation criteria for the solutions of even-order neutral differential equations with a p-Laplacian like operator. The proposed theorems not only provide totally different approach but also essentially improve a number of results reported in the literature. To demonstrate the advantage of our results, we present two examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate oscillatory properties of even-order advanced differential equations. The key idea of our approach is to conduct a comparison with first order equations and use the Riccati transformation technique. Some new oscillation criteria are shown. Two examples are presented in order to clarify the main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex functions. Also, we obtain Hermite Hadamard inequality for fractional integral by using these functions. Finally, some applications of these inequalities are given. [ABSTRACT FROM AUTHOR]

In this paper, a one-to-one correspondence between Bessel sequences and bounded linear operators is provided. This leads to an algebra structure on the set of all Bessel sequences in a separable Hilbert space. Some kinds of frames as special classes of operators are considered. Also, normal Bessel sequences and positive frames are presented. Finally, power means of positive frames are introduced. These allow researches to construct a large number of new frames from existing frames. [ABSTRACT FROM AUTHOR]

The present paper implements the novel generalized (G'/G)-expansion approach in solving the most popular nonlinear wave equations such as the longitudinal wave motion equation in a magneto-electro-elastic circular rod and the Drinfeld-Sokolov-Wilson equation. In this regard, we investigate the method to obtain new type of wave solutions of the studied models. New exact wave solutions are derived in the structures such as singular bright solition, compaction, singular bright periodic wave solitions, singular dark solition and singular dark periodic wave solition solutions of the studied models by using the novel generalized (G'/G)-expansion scheme. To draw the physical aspect of the got results, the 2D, 3D surfaces as well as the relating the contour plot surfaces of some acquired results are performed. The obtained results can assist to illustrate the physical application of the examined models and other nonlinear physical models appearing in mathematical physics. [ABSTRACT FROM AUTHOR]

In this paper the author investigates the global boundedness in Banach Lp spaces of rough semiclassical Fourier integral operators defined by generalized rough Hormander class amplitudes and rough class phase functions which behave in the spatial variable like Lp functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of solutions to conformable stochastic differential equations. Firstly, we show the trivial solution are stochastially stable, stochastically asymptotically stable and almost surely exponentially stable, respectively. Secondly, we show the nontrivial solution are Ulam's type stable in the sense of probabilities. Finally, two examples are given to present the theoretically results. [ABSTRACT FROM AUTHOR]

In this paper, a general fixed point theorem for quasi-contractions in b-metric spaces, which is a sharp improvement of Amini-Harandi's result, Mitrovic and Hussain's result, and is a generalization of many b-metric fixed point theorems in the literature, is proved. The technique overcomes some limits in b-metric fixed point theory compared to metric fixed point theory. The obtained results are also supported by examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite approximate controllability of fractional semilinear differential equations involving the Hilfer derivative. We show that if the linear part is approximate controllable, then under suitable conditions the semilinear system is finite approximate controllable. [ABSTRACT FROM AUTHOR]

Exponential monomials and polynomials are the basic building blocks of spectral synthesis. Recently a systematic study of exponential polynomials has been started on hypergroups. In this paper we join these investigations and describe exponential polynomials on hypergroup joins. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a certain class H λ,a m,q (ξ,M) of normalized analytic functions of complex order connected with a q-analogue of integral operators. For this complex-order analytic function class, we determine a sufficient condition in terms of the coefficients, estimates for the coefficients and a maximization theorem concerning the coefficients. Various consequences and applications of our main results are also considered. A brief remark about the demonstrated equivalence of the q-calculus and the so-called (p,q)-calculus is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate two parameters hk,n and h ' k,n of some P-Q type Theta functions ϕ(q) for any positive real numbers k and n. During this process, we also evaluate Ramanujan's cubic continued fraction. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some a Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, interval estimation for the parameters of the Kumaraswamy distribution is studied based on progressively censoring scheme and the record values. Some pivotal quantities and Theorems are proposed to construct the exact confidence interval for the one-shape parameter and the joint confidence region for the two-shape parameters. Simulation study is performed to investigate the coverage probabilities of the proposed confidence under progressively censored sample and upper record data. Finally, the proposed intervals and regions have been studied based on two real data sets as the illustrative examples. The first data set contains the strength characterization of brittle material and the second data set consists of the daily average wind speeds. [ABSTRACT FROM AUTHOR]

In this paper we generalize the well-known class of quasi contractions pairs, by using the so-called Geraghty's property and by controlling the contractive inequality with an altering distance function. For this class, in the setting of b-metric spaces, we prove the existence and uniqueness a of common fixed point assuming some non commutative notions. Finally, for this class of mappings we prove the b-convergence of the Jungck-Mann iterative scheme under suitable conditions on the b-metric space and on the altering distance function. [ABSTRACT FROM AUTHOR]

The problem of identifying of the several unknown time dependent parameters in the minor coefficient and in the special type right-hand side function of the semilinear higher order ultraparabolic equation from the additional initial, boundary and integral type overdetermination conditions is considered in this paper. The sufficient conditions of the unique solvability on the interval [0;T]; where T is determined by the coefficients of the equation, are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the operator denoted by Dm : A → A, is defined by Dm[ f ](z) = (1 λ)Rm[ f ](z)+lLm[ f ](z), z 2 U, a differential-integral operator, where Rm is Ruscheweyh differential operator and Lm is Libera integral operator. By using the operator Dm the class of univalent functions denoted by M(m,λ,a), 0 ≤ λ ≤ λ 0 ≤ λ a < 1, is defined and several differential subordinations are studied. [ABSTRACT FROM AUTHOR]

In this paper, we study to approximate solutions of quasi-equilibrium problems in Banach spaces, which generalizes equilibrium problems and quasi-variational inequalities. In fact, we prove weak convergence of the sequence generated by the proximal point method to a solution of the quasi-equilibrium problem. Then we show that the generated sequence converges strongly to a solution of the quasi-equilibrium problem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a certain subclass of meromorphic multivalent close-to-convex functions. Such results as coefficient inequalities, and radius of meromorphic convexity are derived. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of an admissible extended Z-contraction mapping in the setting of extended b-metric spaces. As an application, we consider Ulam stability problems based on our contractions. The presented results cover several existing results in the literature. [ABSTRACT FROM AUTHOR]

As pointed out in the monographs [5, 6] on semirings, ideals play an important role despite the fact that they need not be congruence kernels as in the case of rings. Hence, having two commutative semirings S1 and S2, one can ask whether an ideal I of their direct product S = S1 ×S2 can be expressed in the form I1 ×I2 where Ij is an ideal of Sj for j = 1,2. Of course, the converse is elementary, namely if Ij is an ideal of Sj for j = 1,2 then I1 × I2 is an ideal of S1 × S2. Having a congruence Θ on a commutative semiring S, its 0-class is an ideal of S, but not every ideal is of this form. Hence, the lattice IdS of all ideals of S and the lattice KerS of all congruence kernels (i.e. 0-classes of congruences) of S need not be equal. Furthermore, we show that the mapping Θ 7→ [0]Θ need not be a homomorphism from ConS onto KerS. Moreover, the question arises when a congruence kernel of the direct product S1 ×S2 of two commutative semirings can be expressed as a direct product of the corresponding kernels on the factors. In the paper we present necessary and sufficient conditions for such direct decompositions both for ideals and for congruence kernels of commutative semirings. We also provide sufficient conditions for varieties of commutative semirings to have directly decomposable kernels. [ABSTRACT FROM AUTHOR]

In this paper we give a representation formula for the general solution to the following two-dimensional system of difference equations ... where parameters a,b and initial values x-2,x-1,x0,y-2,y-1,y0 are real numbers. We also give some theoretical explanations related to the representation. [ABSTRACT FROM AUTHOR]

In this paper, complex differential equations from first and second order with constant coefficients are solved using reduced differential transform method (RDTM). Such equations were previously solved by other methods. While obtaining a solution with these methods, the solution was reached by dividing the equation into real and imaginary parts. With the RDTM used in this study, we found that the solution can be reached without dividing the real and imaginary parts of the equation. An iteration relation is given for the solution of such equations. In addition, a variable coefficient equation was solved with RDTM. [ABSTRACT FROM AUTHOR]

Let R be a ring with involution. The skew Lie product of a,b R is defined by O[a,b] = ab-ba*. In the present paper we study prime ring with involution satisfying identities involving skew Lie product and left centralizers. [ABSTRACT FROM AUTHOR]

In this paper we introduce the classes Tn (p,λ,A,B) and Kn (p,λ,µ,m,A,B) and derive distortion inequalities of the functions belonging to class Kn (p,λ,µ,m,A,B). Further we apply to the (n,δ)- neighborhoods of functios in the class Kn (p,λ,µ,m,A,B). [ABSTRACT FROM AUTHOR]

In this paper, some existence results for generalized vector equilibrium-like problems (for short, GVELPs) are established by virtue of a generalized KKM-Fan theorem in topological vector spaces. In addition, some applications to vector optimization problems are also given. The results presented in this paper are the extension and improvement of the corresponding results of other authors. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and analyze chaotic and hyperchaotic conservative complex nonlinear systems. These systems appear in several branches of applied sciences. Lyapunov exponents are calculated to observe chaotic and hyperchaotic behaviors. The wide range of systems parameters at which chaotic and hyperchaotic solutions exist is calculated. The modules for complex variables are computed and plotted. The projections of chaotic and hyperchaotic solutions are shown in 3- spaces and 2-planes. The systems of this paper leave rooms for further studies in the near future, e.g. control and several types of synchronization of the solutions of these systems. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings. For this scheme, we prove some convergence theorems in CAT(0) spaces. In process, we remove a restricted condition (also called end-point condition) in previous several existing results. Thus, several relevant results cited in the literature generalize and improve. [ABSTRACT FROM AUTHOR]

In the paper, the authors first introduce a concept "r-mean convex function on coordinates" and then establish several integral inequalities of the Hermite-Hadamard type for r-convex functions and r-mean convex functions on coordinates. [ABSTRACT FROM AUTHOR]

This paper concerns existence and stability of solutions to periodic linear evolution equations with noninstantaneous impulses via the theory of operator semigroup. A series of fundamental results including compactness, semigroup property, exponential estimate and periodicity are established for a new introduced impulsive evolution operator. Moreover, triple sufficient conditions are given to guarantee this impulsive evolution operator is exponentially stable. In addition, a relationship between existence of periodic solutions and fixed point of impulsive evolution operator is determined, and the alternative results on periodic solutions and their asymptotical stability are obtained by using the well known Fredholm alternative theorem. Finally, an example of periodic impulsive parabolic linear partial differential equation is given for illustration of the theoretically results. [ABSTRACT FROM AUTHOR]

This study provides a broad overview of the generalization of the various quaternions, especially in the context of its enhancing importance in the disciplines of mathematics and physics. By the help of bicomplex numbers, in this paper, we define the bicomplex generalized k-Horadam quaternions. Fundamental properties and mathematical preliminaries of these quaternions are outlined. Finally, we give some basic conjucation identities, generating function, the Binet formula, summation formula, matrix representation and a generalized identity, which is generalization of the well-known identities such as Catalan's identity, Cassini's identity and d'Ocagne's identity, of the bicomplex generalized k-Horadam quaternions in detail. [ABSTRACT FROM AUTHOR]

The paper gives multiplicity results for the impulsive boundary value problem x" = f(t,x), for a.e. t ∈ [0,T], such that x(t) ∈ int K, x'(s +) = -x'(s-), if s ∈ (0,T), x(s) ∈ ∂K, x(0) = A, x(T) = B, where K ⊂ R is a compact interal, f is Carathéodory function on [0,T]?× K and A, B ∈ int K. This problem can be understood as a problem in one-dimensional billiard space and it is also a generalization of oscillator with obstacles from below and from above and absolutely elastic impacts. A simple condition for the existence of solution with exact number of impacts is given, as well as the multiplicity result. The results are obtained by a transformation into problem without impulses (without impacts) and using Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper an emergence of leader-following consensus on arbitrary time scales is investigated. It means that the step size is not necessarily constant but it is a function of time. We propose and prove conditions ensuring a leader-following consensus for discrete time scales. The presented results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce and investigate (p,q)-extensions of two bivariate kinds of Bernoulli polynomials and numbers. We firstly examine several (p,q)-analogues of the Taylor expansions of products of some trigonometric functions and determine their coefficients which are also analyzed in detail. Then, we introduce two bivariate kinds of (p,q)- Bernoulli polynomials and acquired multifarious formulas and relations including connection formulas, recurrence formulas, correlations with aforementioned coefficients, partial (p,q)-differential equations and (p,q)-integral representations. [ABSTRACT FROM AUTHOR]

It is well known that for any nonempty closed convex subset C of a Hilbert space, any best approximation y ∈ C of the point x satisfies the inequality ||x-y||² + ||z-y||² ≤ ||x-z||² for all Z ∈ C. In this paper, we first introduce and study a new subset of best approximations involving this inequality in general metric spaces. Then, we provide some equivalent conditions which characterize Hilbert spaces. [ABSTRACT FROM AUTHOR]

Let R be a prime ring with char(R)≠2. A biadditive symmetric map Δ: R×R → R is called symmetric (α, β)-biderivation if, for any fixed y ∈ R, the map x ↦ Δ(x,y) is a (α, β)-derivation. A symmetric biadditive map Γ : R×R → R is a symmetric generalized (α, β)-biderivation if for any fixed y ∈ R, the map x ↦ Γ(x,y) is a generalized (α, β)-derivation of R associated with the (α, β)-derivation Δ(.,y). In the present paper, we investigate the commutativity of a ring having a generalized (α, β)-biderivation satisfying certain algebraic conditions. [ABSTRACT FROM AUTHOR]

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]