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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.

In this paper, we firstly establish an identity by using the notions of quantum derivatives and integrals. Using this quantum identity, quantum Newton-type inequalities associated with convex functions are proved. We also show that the newly established inequalities can be recaptured into some existing inequalities by taking q→1−

In this paper, we introduce a new extensions of Srivastava’s triple hypergeometric functions HAHBHC

In this paper we study a class of p (x)

In this paper, we establish a new version of Hermite–Hadamard type inequality for convex functions. Moreover, we establish a general version of qqqqq

In this paper, we introduce generalized circular surfaces, a generalization of generalized tube surfaces and circular surfaces. Moreover, we define a special dual quaternion by using the moving frame along the spine curve of generalized circular surface. We then show that the screw motion obtained by this dual quaternion can be used to construct generalized circular surfaces. We also prove that these generalized circular surfaces can be expressed by homothetic motions. Finally, we provide some examples of generalized circular surfaces with figures.

In this paper, we prove coincidence point results for a pair of self mappings defined on a metric space employing a comparison function and a locally Tet al.

In this paper, we considered quadratic OKOKOKOKOK

The section 1 of this paper deals with the definition for a pseudo symmetric spacetime. In section 2, it is proved that a (PZS)4Z(PZS)4(PZS)4

In this paper, we solve in closed-form the following third-order system of nonlinear difference equations xn+1= ynyn−1xn−1pxn(anyn−2q+bnynyn−1),yn+1= xnxn−1yn−1qyn(cnxn−2p+dnxnxn−1),p,q∈ℕ,n∈ℕ0 x−i,y−i,i=0,1,2(an)n∈ℕ0,(bn)n∈ℕ0,(cn)n∈ℕ0,(dn)n∈ℕ0

In this paper we introduce two new classes of inverses for square matrices, which are called 1Drazin (in short, 1D) inverse and Drazin1 (in short, D1) inverse. Next, we investigated the existence and uniqueness of 1D inverse and its dual D1 inverse. Some representation and characterizations of these inverses are derived. In addition to this, we obtain some properties of 1D and D1 inverses through idempotent and binary relations.

In this paper we determine distance k--domination number of graph obtained by duplication of vertices altogether by edges in cycle Cn, splitting graph of cycle Cn as well as graph obtained by duplication of edges altogether by vertices in cycle Cn. [ABSTRACT FROM AUTHOR]

In this paper we propose a parallel iterative hybrid methods for finding a common element of the solution sets of a finite family of pseudomonotone equilibrium problems and the fixed points set of a semigroup-nonexpensive mappings in Hilbert spaces. Under mild conditions, we obtain the strong convergence of the proposed iterative process. Some numerical experiments are given to verify the efficiency the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we obtain some Cheeger-Gromov-Taylor type compactness theorems for a forward complete and connected Finsler manifold of dimensional n ≥ 2 via weighted Ricci curvatures. The proofs are based on the index form of a minimal unit speed geodesic segment, Bochner-Weitzenböck formula and Hessian comparison theorem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the additive (α, β)-functional equation ... for all complex numbers α with [α] D 1 and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α, β)-functional equation (0.1) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper we consider the Ln : A → A, Ln f(z) = (1 - λ) Dn f(z) + λIn f (z) linear operator, where Dn is the Sălăgean differential operator and I n is the Sălăgean integral operator. We study several differential subordinations generated by Ln. We introduce a class of holomorphic functions Lnm(β), and obtain some subordination results. [ABSTRACT FROM AUTHOR]

In this paper, we determine the sums ... and some congruences can be obtained by using them. For example, for an odd prime p ≠ 5, ... and for an odd prime p, ... where d ∈ {0, ..., (p-1)/2}, Fn is the nth Fibonacci number, Ln is the nth Lucas number and Pn is the nth Pell number. (./p) denotes the Legendre symbol. [ABSTRACT FROM AUTHOR]

Two common fixed point theorems for a class of contractive mappings are proved in metric spaces. As an application, the existence and uniqueness of solution for a functional equation arising in dynamic programming is given. The results presented in this paper generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we discuss the approach for optimal switching control problem with unknown switching points. The case with unknown switching point is more general and generalizes the results existing in the literature. By using suitable transformation, the main problem is reduced into a problem with known interval and further the unknown boundary of the integral in the minimization functional is reduced to the known one. This fact is illustrated by an example. The reduced problem is solved numerically by using the Gradient Projection Method Algorithm. [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]

The number of formal concepts generated from the input context is an important parameter in the cost functions of concept formation algorithms. The calculation of concept count for any arbitrary context is a hard, NP-complete problem and only rough approximation methods can be found in the literature to solve this problem. This paper introduces an efficient numerical approximation algorithm for contexts where attribute probabilities are independent from the objects instances. The preconditions required by the approximation method are usually met in the FCA applications, thus the proposed method provides an efficient tool for practical complexity analysis, too. [ABSTRACT FROM AUTHOR]

This study is concerned with a singularly perturbed three-point boundary-value problem with delay. Firstly, bounds on the solution and its derivative of the solution to be used later in the paper are obtained. To solve it numerically, we use an exponentially fitted difference scheme on an equidistant mesh which is established by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. Then, the stability and convergence analysis of difference scheme is given and it is uniformly convergent in perturbation parameter. Furthermore, numerical results which show the effectiveness of the method are presented. [ABSTRACT FROM AUTHOR]

In this paper we prove some new results on near-vector spaces and near domains and give a first application of the nearring of quotients with respect to a multiplicative set, namely we construct a new class of near-vector spaces from near domains. [ABSTRACT FROM AUTHOR]

The generalized convexity of the inverse hyperbolic cosine function related to the hyperbolic metric is investigated in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a pair (f, h) called upper class of type II and αβ-contractive mappings. We obtain that all the corresponding established results of Hussain et al. [7] are immediately consequences of our main result. Our main result generalizes and modifies several existing results in literature. Also, an example is given to support the main result. [ABSTRACT FROM AUTHOR]

Our goal is to create a propositional logic formula to model a directed graph and use a SAT solver to analyse it. This model is similar to the well-know one of Aspvall et al., but they create a directed graph from a 2-SAT problem, we generate a 2-SAT problem from a directed graph. In their paper if the 2-SAT problem is unsatisfiable, then the generated directed graph is strongly connected, in our case, if the directed graph is strongly connected, then the generated 2-SAT problem is a black-and-white 2-SAT problem, which has two solutions: where each variable is true (the white assignment), and where each variable is false (the black one). If we see a directed graph as a communication model of a network, then we can ask in our model whether a node can send a message to another one through the network. More specifically we can ask whether all nodes can send messages to all other ones, i.e., the graph is strongly connected or not. [ABSTRACT FROM AUTHOR]

The paper concerns to investigations in the field of differential geometry. It is realized by a method of prolongations and scopes of G.F. Laptev which generalizes a moving frame method and Cartan's exterior forms method and bases on calculation of exterior differential forms. The space Π of centred m--planes is considered in projective space Pn. Principal fiber bundle is arised above Π. An analog of Neifeld's connection is given in this principal fibering. It is proved that the analog of the Norden normalization of the space of centred planes induces Neifeld's connection. The torsion of Neifeld's connection analog is introduced. It is shown, that this object is a tensor. [ABSTRACT FROM AUTHOR]

Let n ≥ 1 be a fixed positive integer and R be a ring. A permuting n-additive map Ω : Rn → R is known to be permuting generalized n-derivation if there exists a permuting n-derivation Δ : Rn → R such that Ω(x1, x2, ⋯,xixi⋯,xn) = Ω(x1, x2, ⋯,xi,⋯xn)xi + xi Δ(x1, x2, ⋯,xi⋯xn) holds for all xi, xi ∈ R. A mapping δ : R → R defined by δ(x) = Δ(x, x, ⋯, x) for all x ∈ R is said to be the trace of Δ. The trace &# of can be defined in ω of Ω can be defined in the similar way. The main result of the present paper states that if R is a (n+1)!-torsion free semi-prime ring which admits a permuting n-derivation Δ such that the trace δ of Δ satisfies [[δ(x), x], x] ∈ Z (R) for all x ∈ R, then ͐ is commuting on R. Besides other related results it is also shown that in a n-torsion free prime ring if the trace ω of a permuting generalized n-derivation is centralizing on R, then ω is commuting on R. [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 the paper, firstly, a new fractional integral identity is obtained. Then, some new results related to the left side of Fejér's inequality for differentiable mappings whose derivatives in absolute value are convex via fractional integral operator, using this identity with fundamental inequalities such as Hölder's integral inequality, power-mean inequality and triangle inequality for integral, are presented. The results presented here would provide extensions of those proved in [11]. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity and M be a unitary R-module. In this paper, we obtain a scheme (X(M),OX(M)) over the primary-like spectrum X(M) of M and prove that (X(M),OX(M)) is a Noetherian scheme when R is a Noetherian ring. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe the solution (f,g) of the equation = , x,y ∣ X, where f:X→Y , g:X→X, X,Y are inner product spaces over the same field K ∣ {R,C}. [ABSTRACT FROM AUTHOR]

In this paper we obtain some new integral inequalities like Hermite-Hadamard type for log-convex functions and P-functions. [ABSTRACT FROM AUTHOR]

In this paper, we generalize β* relation on submodules of a module (see [1]) to elements of a complete modular lattice. Let L be a complete modular lattice. We say a;b ∊ L are β* equivalent , aβ*b, if and only if for each t ∊ L such that a⋁t = 1 then b⋁t = 1 and for each k ∊ L such that b⋁k D1 then a⋁k D1, this is equivalent to a⋁b⪡1=a and a⋁b⪡1=b. We show that the β* relation is an equivalence relation. Then, we examine β* relation on weakly supplemented lattices. Finally, we show that L is weakly supplemented if and only if for every x ∊ L, x is equivalent to a weak supplement in L. [ABSTRACT FROM AUTHOR]

Recently, B. Samet et al. (Fixed Point Theory and Appl. 2013:5, 2013, doi:10.1186/1687-1812-2013-5) has introduced the concept of new contraction mappings and obtained results on the fixed point for nonlinear contractive mappings in a metric space. In the present paper, we introduce the concept of a new contraction via the measure of non-compactness on a Banach space, we obtain a few generalizations of Darbo fixed point theorem and extend some recent results of Aghajani et al. We also show the applicability of obtained results to the theory of integral equations. [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]

In this paper, by using umbral calculus and umbral algebra methods, we derive several interesting identities and relations related to the modified and unification of the Bernoulli, Euler and Genocchi polynomials and numbers and the generalized (β-) Stirling numbers of the second kind. We also give some applications and remarks related to these numbers and polynomials. [ABSTRACT FROM AUTHOR]

In this paper using the (p,k)-parametrization of theta functions and Eisenstein Series, developed by Alaca, Alaca and Williams, we obtain some new theta function identities and then use them to derive explicit formulae for the number of representations of a positive integer n by certain quadratic forms 6Σk=1 ak(x22k-1+x2k-1x2k+x22k/ in twelve variables where ak ∊ {1,2,4}. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the concept of partially ordered rectangular metric spaces using the notation (X,≤d). Also, we give a generalized contractive condition in the context of partially ordered rectangular metric space for all comparable pair of X. Our results extend and generalize the well-known results of [13], [1], [14] and [11]. [ABSTRACT FROM AUTHOR]

In this paper, the order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials (q > 0) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∊ C : ∣z∣ < R}, R > q, the rate of approximation by the q- Durrmeyer - Stancu operators (q > 1) is of order q-n versus 1/n for the classical q-Durrmeyer - Stancu operators. [ABSTRACT FROM AUTHOR]

In this paper, we show that there is no solution of the diophantine equation uk1+ uk2 +...+ukn-1 = uln+1+uln+2+...+uln+rr for special cases of k and l where the elements of sequence fung satisfy the relation un = Aun-1 - un-2 with u0 = 0, u1= 1 and A ≥ 3 is a positive integer. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the double inequality Mα(a,b) < NGQ(a,b) 0 with a ≠ b if and only if α ≤ 2log2/(5log2-2logπ) = 1:1785... and β ≥ 4/3,where NGQ(a,b) = [G(a,b)CQ2(a,b)=U(a,b)]/2 is the second Neuman mean, G(a,b) = √ab, Q(a,b) = √(a2+b2)/2 and U(a,b) = (a-b)/[√2tan-1((a - b)/ √2ab)] are the geometric, quadratic and Yang mean of a and b, respectively( [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]

Let R be a ring and M be a left R-module. M is called cofinitely weak δ-supplemented (or briefly δ- CWS-module) if every cofinite submodule of M has a weak δ-supplement in M. In this paper, we give various properties of this kind of modules. It is shown that a module M is δ-CWS-module if and only if every maximal submodule has a weak δ-supplement in M. The class of cofinitely weak δ-supplemented modules are closed under taking homomorphic images, arbitrary sums and short exact sequences. Also we give some conditions equivalent to being a δ-CWS-module for a δ-coatomic module. [ABSTRACT FROM AUTHOR]

In this paper, an effort has been made to improve the notion of α-Geraghty contraction type mappings and establish some common fixed point theorems for a pair of α-admissible mappings under the improved approach of generalized rational α-Geraghty contractive type condition in a complete metric space. An example has been constructed to demonstrate the novelty of these results. [ABSTRACT FROM AUTHOR]

This work focuses on the class of multivalued regularized equilibrium problems in the context of uniformly prox-regular sets introduced and studied in [Noor, M.A.: Multivalued regularized equilibrium problems. J. Global Optim. 35, 483-492 (2006)]. The algorithms and results presented in the paper cited above are investigated and analyzed and some fatal errors in them are detected. Meanwhile, the correct version of the corresponding algorithm and results is given. [ABSTRACT FROM AUTHOR]

In the present paper, new subclasses of bi-univalent functions of complex order associated with the (p,q)-derivative are introduced. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of functions belonging to these classes. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some results concerning permuting triderivations and permuting generalized triderivations on prime and semiprime rings which partially extend some results contained in [9] and [10]. [ABSTRACT FROM AUTHOR]

In this paper, the exponential dichotomy, and Tikhonov and Banach fixed point theorems are used to study the existence and uniqueness of pseudo almost periodic solutions of nonhomogeneous iterative functional differential equations of the form x'(t)= λ1(t)x(t)+ λ 2(t)x[2](t)+...+λn(t)x[n](t)x[n](t)+f(t). [ABSTRACT FROM AUTHOR]

In this paper, we establish Lp-Brunn-Minkowski inequality for dual Quermassintegral of Lp-mixed intersection bodies. As application, we give the well-known Brunn-Minkowski inequality for mixed intersection bodies. [ABSTRACT FROM AUTHOR]