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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, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejér inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard- Fejer inequality and better than given in [9] by Sarıkaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kırmacı. [ABSTRACT FROM AUTHOR]

In this paper, we study exact null controllability of Hilfer fractional semilinear stochastic differential equations in Hilbert spaces. By using fractional calculus and fixed point approach, sufficient conditions of exact null controllability for such fractional systems are established. An example is given to show the application of our results. [ABSTRACT FROM AUTHOR]

In present paper, by proving a new integral identity, using Hölder's inequality and mathematical analysis, we prove some Hermite-Hadamard type integral inequalities for geometrically quasi-convex functions which give better estimates to those already proven for the rightside of a Hermite-Hadamard type inequality established for geometrically convex functions in earlier works. A numerical example is also provided to support our claim. Applications of the results to special means of positive real numbers are given. [ABSTRACT FROM AUTHOR]

A graph G is called a fractional ID-k-factor-critical graph if after deleting any independent set of G the resulting graph admits a fractional k-factor. In this paper, we prove that for k≥2, G is a fractional ID-k-factor-critical graph if δ(G) ≥n/3+k,σ2(G)≥4n/3,n≥6k-8 The result is best possible in some sense. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the oscillations in forced second order nonlinear differential equations with nonlinear damping terms. By using clasical variational principle and averaging technique, new oscillation criteria are established, which revise, improve and extend some recent results. Furthermore our study answers the comment [16]. Examples are also given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, two Marx-Strohhäcker type results are proven for a certain class of analytic and multivalent functions in the open unit disk D. The first result gives the order of multivalent starlikeness for multivalently convex functions of some specified order. The second result provides a lower bound over the unit disk D of R (f(z)/zp) for functions f (z) that are multivalently starlike of a given order. Relevant connections of the results presented here with earlier results are also indicated. [ABSTRACT FROM AUTHOR]

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations. [ABSTRACT FROM AUTHOR]

The paper deals with problem on asymptotic solutions to a system of singular perturbed linear differential-algebraic equations. Case of multiple roots of a characteristic equation is studied. Technique of constructing the asymptotic solutions is developed. [ABSTRACT FROM AUTHOR]

This paper deals with the Sturm-Liouville equation with a finite number of point δ-interactions and eigenvalue parameter contained in the boundary condition. Sturm-Liouville problem with discontinuities at one or two points and its different variants have already been investigated. In this study we extend these results to a finite number of point δ-interactions case. The crucial part of this study is the using graph demonstration to obtain asymptotic representation of solutions. [ABSTRACT FROM AUTHOR]

Let...be the sequence of partial sums of generalized and normalized Struve functions...The purpose of the present paper is to determine lower bounds...Furthermore, we give lower bounds for R...where κ[fv,d,c] is the Alexander transform of fv,d,c. [ABSTRACT FROM AUTHOR]

This paper deals with the study of the generalized hypergeometric matrix function and obtains some of its properties. We rephrase some results from the previous (earlier) works that will be used in this study. We get the hypergeometric matrix function representation, matrix differential equation, generating matrix functions, bilinear generating matrix functions, matrix recurrence relations, finite summation formulas and related results for the Konhauser matrix polynomials given in [34]. Finally, we give some important results involving properties of Mittag-Leffler and Bessel-Maitland matrix functions as applications. [ABSTRACT FROM AUTHOR]

In this paper, we obtained some fixed point results for continuous mappings satisfying a generalized contractive condition in the setting of two metrics space endowed with a binary relation. Our theorems generalize and extend several known results in the literature. As application, we establish an existence theorem for the solution of a nonlinear first order differential equation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of linear systems of neutral differential equations with delay. Assuming the linear parts to be given by pairwise permutable matrices, representation of a solution of a nonhomogeneous initial value problem using matrix polynomial of a degree depending on time is derived. Examples illustrating the obtained results are given. [ABSTRACT FROM AUTHOR]

In this paper we consider a problem for the first order Dirac differential equations system with spectral parameter dependent on boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this system are investigated. The expansion formula with respect to eigenfunctions is obtained and Parseval equality is given. The main theorem on necessary and sufficient conditions for the solvability of inverse problem is proved and the algorithm of reconstruction of potential from spectral data (the sets of eigenvalues and normalizing numbers) is given. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the growth and oscillation of solutions and their derivatives of equations of the type f''+ A(z) f' + B(z) f = F(z), where A(z), B(z) (≢0) and F(z) (≢0) are meromorphic functions of finite order. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm- Liouville problem together with two supplementary transmission conditions at one interior point. Further we develop Green's function method for spectral analysis of the considered problem in modified Hilbert space. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of solutions for a sequential fractional differential equation of arbitrary order ξ + 1; ξ ∊ (n-1, n), n ⩾ 2 with three-point nonlocal boundary conditions. We make use of standard tools of fixed point theory to establish our existence results. An illustrative example and some special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of solution for a multi-term arbitrary (fractional) order differential equation with some nonlocal and integral conditions. [ABSTRACT FROM AUTHOR]

This paper focuses on the problems of a diagonal common quadratic Lyapunov function (DCQLF) existence for sets of stable positive linear time-invariant (LTI) systems. We derive the equivalent algebraic conditions to verify the existence of a DCQLF, namely that the finite number Hurwitz Mezler matrices at least have a common diagonal Stein solution. Finally some reduced cases are considered. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for boundary value problems of fractional differential equations of order q ∊ (0, 1] with four-point integral boundary conditions. Existence and uniqueness results are obtained by using well known fixed point theorems. Some illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the quasilinearization for Riemann-Liouville fractional differential equations with two point boundary condition. By establishing a new comparison principle we get a monotone sequence which converges quadratically to the unique solution of the fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of eventually positive (negative) and oscillatory solutions to the following nonhomogeneous second order delay differential equation ... where p and f are suitable real functions. [ABSTRACT FROM AUTHOR]

This paper covers several topics that involve symmetries of differential equations: from the connection between Lie symmetries and Jacobi last multiplier with a detour to the inverse problem of calculus of variations, to the importance of maximal group of Noether symmetries on the road from classical to quantum mechanics. [ABSTRACT FROM AUTHOR]

By the work of Abu Muriefah, Al-Rashed, Dujella and the author, the problem of the existence of D(z)-quadruples in the ring ℤ[√-2] has been solved, except for the cases z = 24a + 2 + (12b + 6) √-2,z = 24a + 5 + (12b + 6) √-2, z = 48a = 44 + (24b + 12) √-2. In this paper, we present some new formulas for D(z)-quadruples in these remaining cases, involving some congruence conditions modulo 11 on integers a and b. We show the existence of D(z)-quadruple for significant proportion of the remaining three cases. [ABSTRACT FROM AUTHOR]

In this paper, the existence of solutions of some minimization problems for noncyclic mappings in G—metric spaces is studied. Our results can be considered as an extension of Abkar and Gabeleh's result [Global Optimal Solutions of Noncyclic Mappings in Metric Spaces, J. Optim. Theory. Appl. 153 (2011), 298-305] to the case of G群metric spaces. [ABSTRACT FROM AUTHOR]

Let n×n complex matrices P and Q be nontrivial generalized reflection matrices, i.e., P* = P = P-1 ≠ In, Q* = Q = Q-1 ≠ In. A complex matrix A with order n is said to be a (P, Q) generalized anti-reflexive matrix, if PAQ = -A. We in this paper mainly investigate the (P, Q) generalized anti-reflexive maximal and minimal rank solutions to the system of matrix equation AX = B. We present necessary and sufficient conditions for the existence of the maximal and minimal rank solutions, with (P, Q) generalized anti-reflexive, of the system. Expressions of such solutions to this system are also given when the solvability conditions are satisfied. In addition, in correspondence with the minimal rank solution set to the system, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided. [ABSTRACT FROM AUTHOR]

In this paper, we give a recurrence relation for the Tribonacci numbers with indices in aritmetics progression, {Trn+s} for 0 ⩽ s < n. We find sums of {Trn} for arbitrary integer r via matrix methods. [ABSTRACT FROM AUTHOR]

In this paper we introduce the Mittag-Leffler operators, which includes the modified Szász-Mirakjan operators. We obtain the transformation properties and compute the rate of convergence by using modulus of continuity. Furthermore we give the A-statistical approximation theorem for these operators. [ABSTRACT FROM AUTHOR]

Let R be a prime ring. By a generalized derivation we mean an additive mapping g : R → R such that g(xy) = g(x)y + xd(y) for all x, y ∈ R where d is a derivation of R. In the present paper our main goal is to generalize some results concerning derivations of prime rings to generalized derivations of prime rings. [ABSTRACT FROM AUTHOR]

In this paper, we present some common fixed point theorems for (ψ, φ)-generalized f - weakly contractive mappings in metric and ordered metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper positive linear set valued maps defined on the cone are studied. The representation theorem for positive linear set valued maps is given and Lipschitz continuity of these maps is proved. The estimations of upper and lower norms of the positive linear set valued maps are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we use the notion of ideal to obtain two more general concepts and call them as I-A-statistical convergence and ideal A-summability. We also use the the concept of I-A-statistical convergence to prove a Korovkin type approximation theorem for double sequences of positive linear operators and present an interesting example to show that our Korovkin theorem is stronger than those proved earlier. [ABSTRACT FROM AUTHOR]

The aims of this paper are introduce the notions of symmetric bi-derivation and generalized derivation in MV-algebras and investigate some of their properties. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalization of the Stancu- Schurer operators based on q-integers and get a Bohman-Korovkin type approximation theorem of these operators. We also compute the rate of convergence by using the first modulus of smoothness and give some numerical result of operators based on Matlab algorithms. [ABSTRACT FROM AUTHOR]

In the present paper we have proved a more general theorem dealing with ∣A, pn∣k summability by using almost increasing sequence. This theorem also includes several known results. [ABSTRACT FROM AUTHOR]

In this paper we investigate a family of second order differential equations which can be considered as the continuous versions of the Fletcher-Reeves iteration for minimization applied to a regularized and penalized convex programming problem. We show that synchronizing the parameter functions of the differential equation the stationary limit point of the trajectories is the minimal norm solution of the given convex programming problem. [ABSTRACT FROM AUTHOR]

In this paper we present the problem of global controllability (GC) of a set of fractional differential equation (SFDE). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain some new sufficient conditions which guarantee the instability of the trivial solution of some certain nonlinear vector differential equations of fourth order. Our results improve and include some well known instability results, which were established on the instability of the trivial solution of certain scalar differential equations of fourth order, to certain nonlinear vector differential equations of fourth order. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of nontrivial symmetric solution for the secondorder three-point boundary value problem for a function ∫ ; [0,1] × R→ R which is continuous and f (t,·) is symmetric on [0, 1]. We shall formulate conditions on ∫ which guarantee the existence of nontrivial symmetric solution. As an application, we also give some examples to demonstrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of a unique solution on a semi-infinite interval for quadratic integral equations with linear modification of the argument in Fréchet spaces using a nonlinear alternative of Leray-Schauder type for contraction maps in Fréchet spaces. [ABSTRACT FROM AUTHOR]

In this paper we prove existence results for boundary value problems for higher-order differential inclusion x(n) (t) ϵ F(t, x (t)) with nonlocal boundary conditions, where F is a compact convex L¹-Carathéodory multifunction. [ABSTRACT FROM AUTHOR]