Search

The authors have recently introduced a new generalized derivative operator μλ1,λ2n,m, that generalized many well-known operators. The trend of finding new differential or integral operators has attracted widespread interest. The aim of this paper is to use the relation ... to discuss some interesting results by using the technique of differential subordination. The results include both subordination and inclusion. In the case of n = 0,λ2 = 0, we obtain the results of Oros [11]. [ABSTRACT FROM AUTHOR]

In this paper, we study the statistical approximation properties of real and complex Post-Widder operators based on q-integers. We also obtain a Voronovskaya-type formula in statistical sense for these operators. [ABSTRACT FROM AUTHOR]

In this paper, nonlocal Cauchy problems for fractional evolution equations involving Volterra-Fredholm type integral operators are investigated. Some new existence theorems of mild solutions are presented by using fractional calculus, Hölder inequality, Beta function and fixed point theorems. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, and let n > 1 be an integer. A proper submodule N of an R-module M will be called 2-absorbing [resp. n-weakly prime], if r; s ∊ R and x ∊M with rsx ∊ N [resp. rsx ∊ N\(N :M)n-1N] implies that rs ∊ (N :M) or rx ∊ N, or sx ∊ N: These concepts are generalizations of the notions of 2-absorbing ideals and weakly prime submodules, which have been studied in [3, 4, 6, 7]. We will study 2-absorbing and n- weakly prime submodules in this paper. Among other results, it is proved that if (N:M)n-1N ≠ (N:M)2N; then N is 2-absorbing if and only if it is n-weakly prime. [ABSTRACT FROM AUTHOR]

In this paper we shall establish sufficient conditions for the existence of solutions of the integral equation of Volterra type and for its solvability in Banach space and CL: The main tools used in our study are the nonexpansive operator technique, contraction principle and Schaefer's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we give general formulas for some weighted binomial sums, using the powers of terms of certain binary recurrences. As an applications of our results, we show that the weighted binomial sums of the generalized Fibonacci and Lucas numbers can be expressed via the second kinds of Chebyshev polynomials and Stirling numbers. [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]

This paper is concerned with the existence of viable or monotone solutions of a first order functional differential inclusion in a separable Banach space. We consider two cases with moving constraints. [ABSTRACT FROM AUTHOR]

The object of this paper is to study the properties of flat spacetimes under some conditions regarding the W2-curvature tensor. In the first section, several results are obtained on the geometrical symmetries of this curvature tensor. It is shown that in a spacetime with W2- curvature tensor filled with a perfect fluid, the energy momentum tensor satisfying the Einstein's equations with a cosmological constant is a quadratic conformal Killing tensor. It is also proved that a necessary and sufficient condition for the energy momentum tensor to be a quadratic Killing tensor is that the scalar curvature of this space must be constant. In a radiative perfect fluid, it is shown that the sectional curvature is constant. [ABSTRACT FROM AUTHOR]

In this paper, we prove endpoint boundedness of multilinear commutators of Littlewood-Paley operators. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to derive a new inequality of Ostrowski-Grüss type with a parameter involving functions of two independent variables. [ABSTRACT FROM AUTHOR]

In this paper, we improve and further generalize some Čeby&3x0161;ev type inequalities involving functions whose derivatives belong to Lp spaces via certain integral identities. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional linear conjugate Volterra integral equations containing super-singularities in the kernels are considered. The existence of a unique solution in a certain function class is established. Formulas representing the solution are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce q-Szász Schurer operators and calculate their moments. The transformation properties, Korovkin type approximation theorem and rate of convergence of the operators are studied. We further obtain global estimates for q??Szász Schurer operators in terms of some Lipschitz classes. [ABSTRACT FROM AUTHOR]

This study is the continuation of our former work [O. Duman and E. Erkusş, Comput. Math. Appl. 52 (2006) 967-974] in which we obtained a statistical Korovkin-type approximation theorem for a sequence of positive linear operators defined on the space of all real-valued continuous and 2π periodic functions on the real m-dimensional space. In this paper, we compute the statistical rates of this statistical approximation. [ABSTRACT FROM AUTHOR]

The paper treats a linear overdetermined system which contains second order hyperbolic equations with two linear super singularities. The authors obtain some new integral representations of the solutions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to refine some inequalities related to the constant e: Finally, a strengthened Carleman's inequality is given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a Korovkin-type approximation theorem on Hw (I2) , which is the subspace of all continuous and bounded real valued functions on I2 = [0,∞) x [0,∞ by using A-summation process. [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]

In this paper, we extend the preconditioners of Sturler and Liesen [SIAM J. Sci. Comput., 26(2005): 1598-1619]. The spectral characteristics of the preconditioners are investigated and the results show that all eigenvalues of the preconditioned matrices are strongly clustered. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners. [ABSTRACT FROM AUTHOR]

In the present paper, we give a common fixed point theorem for two weakly increasing mappings on ordered Hausdorff uniform spaces, using the distance p: Two multivalued versions of this result are also presented. [ABSTRACT FROM AUTHOR]

In this paper we study the relationship between the generalized Lucas polynomials and the Euler numbers and give several interesting identities involving them. [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]

The aim of this paper is to investigate certain results on 3-prime near-rings and generalize these results on near-rings to semi-group ideals of 3-prime near-rings. [ABSTRACT FROM AUTHOR]

In this paper we discuss the multilinear commutators of singular integral operators on spaces of homogeneous type. By using Hölder's inequalities and the (Lp,Lq) type boundedness of fractional integral operators on spaces of homogeneous type, we obtain that this kind of multilinear commutators is bounded from Lp to Lq, from Lp to Triebel-Lizorkin spaces and from Hb→p to Lp. We also establish their H Kq1,bα,p→, Kq2α,p) type boundedness on spaces of homogeneous type. [ABSTRACT FROM AUTHOR]

The degree distance, Zagreb coindices and reverse degree distance of a connected graph have been studied in mathematical chemistry. In this paper some new extremal values of these topological invariants over some special classes of graphs are determined. [ABSTRACT FROM AUTHOR]

In this paper, we establish p-Minkowski inequality for mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complex oscillation of the nonhomogeneous linear differential polynomial gf = d1f′ + d0f + b. Here d0 (z), d1 (z), b (z) are meromorphic functions such that at least one of d0 (z) and d1 (z) does not vanish identically with ρp (dj) <∞ (j = 0;1), ρp (b) < ∞, and f is a solution of the differential equation f″ + A(z) f = 0, where A(z) is a transcendental meromorphic function with finite iterated order ρp (A) = ρ > 0. [ABSTRACT FROM AUTHOR]

In this paper we use fuzzy α-sets in order to obtain certain characterizations and properties of upper (or lower) fuzzy α-continuous multifunctions. [ABSTRACT FROM AUTHOR]

In this paper we introduce the multiple Mathieu .a; /-series. We obtain two integral representations for multiple Mathieu .a; /-series applying Ivanov’s and then Pog´any’s variant of multiple Euler-Maclaurin summation formula. Then, a bilateral bounding inequality is derived by virtue of the achieved integral expressions. Finally, the special case of multiple Mathieu .a; /-series, the multiple Mathieu a-series has been investigated. [ABSTRACT FROM AUTHOR]

In this paper, for a general modification of the classical Sz´asz-Mirakjan-Kantorovich operators, we obtain many local approximation results including the classical cases. In particular, we obtain a Korovkin theorem, a Voronovskaya theorem, and some local estimates for these operators. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish new sharp upper and lower bounds for the gamma and digamma functions, starting from the Stirling's formula. [ABSTRACT FROM AUTHOR]

This paper concerns the study of the quenching time of the solution of the initialboundary value problem for a system of reaction-diffusion equations. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (ϕq- positivity) for non-cooperative systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new types of sets called (1,2)*-D(α,p) sets, (1,2)*-D(α,s) sets, (1,2)*-D(c,α) sets, (1,2)*-D(c,s) sets and (1,2)*-D(c,p) sets and new classes of mappings called (1,2)*-D(α,p) continuous, (1,2)*-D(α,s) continuous, (1,2)*-D(c,α) continuous, (1,2)*-D(c,s) continuous and (1,2)*-D(c,p) continuous mappings. We obtain several characterizations of these classes, study their bitopological properties, and investigate their relation with other bitopological sets and mappings. [ABSTRACT FROM AUTHOR]

The aim of this research paper is to establish the following summation formula for the Clausen's series 3F2: (Multiple line equation(s) cannot be represented in ASCII text), where f = c(1+a-b)/(a-c), in three different ways. For c = 1/2a, we have (Multiple line equation(s) cannot be represented in ASCII text), which is already available in the literarute. Our formula is then applied to obtain two general results, one is the Euler's transformation for the series 2F2 and another is the Kummer-type first transformation for the series 2F2 established recently by Paris by following a different method. The results obtained generalize the related results by Exton. [ABSTRACT FROM AUTHOR]

For an algebra A, the lattice Quord A of all quasiorders of A, i. e., of all reflexive and transitive relations compatible with all fundamental operations of A, is dealt with. In the present paper we prove that if A is a monounary algebra, then Quord A is distributive if and only if it is modular and we find necessary and sufficient conditions for A under which Quord A is distributive. [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]

J. C. Robson has investigated the ideal In of all polynomials in the free associative algebra R(χ) over a non-commutative ring R generated by χ and the n² entries of an n × n matrix α = (αij), which are satisfied by . He found four cubics generating the ideal for n D 2 and proved its finite generation for any n. Ts. Rashkova has considered the ideal I2 for matrix algebras with involution over a noncommutative ring and over a field of characteristic zero. In the paper the ideal I3 is described for some special upper triangular matrices over a field of characteristic 0. The T -ideal T (U2(G)) is investigated as well for G denoting the infinite dimensional Grassmann algebra. [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]

The aim of this paper is to present a class of linear positive operators of discrete type and its statistical approximation properties obtained by using a Bohman-Korovkin type theorem. [ABSTRACT FROM AUTHOR]

In [4], Dontchev introduced and investigated a new notion of continuity called contra-continuity. Recently, Jafari and Noiri [8-10] introduced new generalizations of contra-continuity called contra-α-continuity contra-super-continuity and contra-precontinuity. Recently, Ekici and Noiri [6] have introduced a new class of continuity called contra δ-precontinuity as a generalization of contra-continuity. In this paper, we obtain some more properties of contra δ-precontinuous functions. [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]