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In this paper, we consider the Fibonacci conditional sequence {fn} and the Lucas conditional sequence flng. We derive some properties of Fibonacci and Lucas conditional sequences by using the matrix method. Our results are elegant as the results for ordinary Fibonacci and Lucas sequences. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of contraction: the almost local contractions. Then, we prove the existence and uniqueness of a fixed-point for local almost contractions in two cases: with constant and variable coefficients of contraction. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of ∣ R, p∣ k,k ≥ 1 integrability of improper integrals and by this definition we prove a theorem, that generalizes a theorem of Orhan. [ABSTRACT FROM AUTHOR]

In this paper we study the modified Hadamard product properties of certain class of analytic functions with varying arguments defined by Ruscheweyh derivative. The obtained results are sharp and they improve known results. [ABSTRACT FROM AUTHOR]

The main object of this paper is to study an old problem concerning the hyper-sums of powers of integers. First, we establish some important properties of this problem (generating function, explicit formula, congruence). Finally, an explicit formula for the hyper-sums of powers of integers involving the generalized Bernoulli polynomials are also given. [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 introduce r-parameter Srivastava polynomials in r-variable by inserting new indices. These polynomials include the Lagrange polynomials in several variables, which are also known as Chan-Chyan-Srivastava polynomials (W.-C.C. Chan, C.-J. Chyan and H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transforms and Special Functions, 12 (2001) 139-148). We prove several two sided linear generating relations between r-variable and (r-1)-variable Chan-Chyan-Srivastava polynomials. Some special cases of the main results are also presented. [ABSTRACT FROM AUTHOR]

In this paper we extend the notion of Melham sum to the Pell and Pell-Lucas sequences. While the proofs of general statements rely on the binomial theorem, we prove some spacial cases by the known Pell identities. We also give extensions of obtained expressions to the other recursive sequences. [ABSTRACT FROM AUTHOR]

In the present paper we concentrate on a natural generalization of NC-McCoy rings that is called J-McCoy and investigate their properties. We prove that local rings are J-McCoy. For a ring R, R[[x]] is J-McCoy if and only if R is J-McCoy. Also, for an abelian ring R, we show that R is J-McCoy if and only if eR is J-McCoy, where e is an idempotent element of R. Moreover, we give an example to show that the J-McCoy property does not pass MnR/, but S.R; n/;A.R; n/;B.R;n/ and T .R;n/ are J-McCoy. [ABSTRACT FROM AUTHOR]

In this paper, we study q-extension of Mittag-Leffler operators. We establish moments of these operators and estimate convergence results with the help of classical modulus of continuity. Also, we give weighted approximation property and A-statistically convergence of the operators L(β)n,q. [ABSTRACT FROM AUTHOR]

Let k≥3 be an odd integer. In this paper, we investigate all positive integer solutions of the equations x4-kx2y+y2=∓A, x4-kx2y+y2=∓A(k2-4), x4-(k2-4)y2=∓4A, and x2-(k2-4)y4=∓4A with A=∓(k∓2). We show that if k≡1(mod8) and k2-4 be a squarefree integer, then the equation x4-kx2y+y2=(k-2)(k2-4) has no positive integer solutions. Moreover, if k2-4 be a squarefree integer, then the equation x4-kx2y+y2=-(k+2)(k2-4) has no positive integer solutions. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring and L is a Lie ideal of R such that LZ(R). A map F:R⋺R is called a multiplicative generalized derivation if there exists a map d:R⋺R such that F(xy)=F(x)y+xd(y), for all x,y∈R. In the present paper, we shall prove that d is a commuting map on L if any one of the following holds: i) F(uv)=±uv, ii) F(uv)=±vu, iii) F(u)F(v)=±uv, iv) F(u)F(v)=±vu, v) F(u)F(v)±uv∈Z, vi) F(u)F(v)±vu∈Z, vii) [F(u),v]±[u,G(v)]=0, for all u,v∈L. [ABSTRACT FROM AUTHOR]

Recently Melham [1] gives closed formulæ for certain finite reciprocal sums. In this paper, we present a different approach to compute these sums in closed form. Our approach is straight-forward and simple. First we convert the sums in q-notation, then use partial fraction decomposition and telescoping to derive closed formulæ. [ABSTRACT FROM AUTHOR]

In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and Hölder type functions etc. These results give us an elegant method for obtaining a number of inequalities for various kinds of fractional integral operators such as for the Riemann-Liouville fractional integral operator, the Hadamard fractional integral operator, fractional hyperqeometric integral and corresponding q-integrals. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove new trigonometric and hyperbolic inequalities, which constitute refinements or analogs of famous Cusa-Huygens, Wu-Srivastava, and related inequalities. Most of the results are sharp. [ABSTRACT FROM AUTHOR]

In this paper a compactness criterion in weighted variable Lebesgue spaces is proved. In particular, are proved a compactness criterion in variable exponent sequence Lebesgue spaces. [ABSTRACT FROM AUTHOR]

In this paper we introduce a class of quasipolar rings which is a generalization of J -quasipolar rings. Let R be a ring with identity. An element a ϵ 2 R is called 1-quasipolar if there exists p2 = p ϵ comm2(a) such that a + p is contained in δ(R), and the ring R is called δ-quasipolar if every element of R is δ-quasipolar. We use 1-quasipolar rings to extend some results of J-quasipolar rings. Then some of the main results of J-quasipolar rings are special cases of our results for this general setting. We give many characterizations and investigate general properties of 1-quasipolar rings. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to transpose some of the results regarding the coupled fixed point theory, developed by Bhaskar and Lakshmikantham [7], using the approaches of Ben-El-Mechaiekh [2], Asgari, Mousavi [1] and Berinde [3]. The first approach replaces the partial order relation from the Ran-Reurings fixed point theorem [10] with a transitive one, the second one uses a reflexive-only relation and whereas the third one introduces the tripled fixed points. Our aim is to obtain some generalized fixed point theorems, containing a more simple symmetrical condition, also extending them for the case of tripled fixed point. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove common fixed point theorems for two operators without the assumption of continuity on a set endowed with vector-valued b-metric and we also study the case of two vector-valued b-metrics. The well-posedness of the fixed point problem is also discussed and an application is presented for systems of operator equations in complete b-normed vector space. Our results improve and generalize theorems 2 and 5 of M. Boriceanu [5]. [ABSTRACT FROM AUTHOR]

In this paper we study the preserving of Riemannian and Ricci tensors with respect to a diffeomorphism of spaces with affine connection. We consider geodesic and almost geodesic mappings of the first type. The basic equations of these maps form a closed system of Cauchy type in covariant derivatives. We determine the quantity of essential (substantial) parameters on which the general solution of this problem depends. [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]

In this paper, we shall introduce the concepts of FG-contraction and ψG-contraction in uniform space endowed with graph to investigate the existence of a fixed point of mappings satisfying these notions. We shall also introduce a common fixed point theorem for pair of mappings satisfying the notion of ψG-contraction in uniform space endowed with graph. [ABSTRACT FROM AUTHOR]

In this paper, some algebraic properties of the joint k-numerical radius, joint k-radius and the joint k-norm of matrices are investigated. Moreover, using the joint higher numerical ranges of diagonal matrices which are convex polyhedrons, a description for the shape of the higher numerical ranges of matrix polynomials is given. [ABSTRACT FROM AUTHOR]

In this paper, the authors improve some results on the existence of at least three weak solutions for non-homogeneous systems. The proof of the main result relies on a recent variational principle due to Ricceri. [ABSTRACT FROM AUTHOR]

In this paper, we have established Hermite-Hadamard-type inequalities for fractional integrals and will be given an identity. With the help of this fractional-type integral identity, we give some integral inequalities connected with the left-side of Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals. [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]

In this paper, the author uses the generating function for the Bernoulli numbers in order to obtain a new proof for a known linear recurrence relation of the Riemann zeta function with even integer arguments, ζ (2n). [ABSTRACT FROM AUTHOR]

Let R be a finite commutative ring and R* be the group of units of R. The unitary Cayley graph of R, denoted by G(R), is the graph obtained by setting all the elements of R to be the vertices and defining vertices x and y to be adjacent if and only if x-y ∈ R*. We denote by Γ (R) the induced subgraph of G(R) whose vertex set is R*. In this paper, the basic properties of Γ (R) are investigated and some characterization results regarding connectedness, chromatic number, chromatic index, girth and planarity of Γ (R) are given. In addition, by using the concept of spectrum of graphs, it is shown that for two finite commutative rings R and S, if Γ (R) is non empty, then Γ (R) ≅(S) as graphs if and only if R/J(R) ≅ S/J(R) as rings, where J(R) and J(S) are the Jacobson radicals of R and S, respectively. As a consequence of this result, we obtain that the structure of a reduced ring R can be determined by Γ (R). [ABSTRACT FROM AUTHOR]

In this paper, we study the r-Jacobi-Stirling numbers of the second kind introduced by Gelineau in his Phd thesis. We give, upon using combinatorial and analytic arguments, the ordinary generating function of these numbers, two recurrence relations, their exact expressions and the log-concavity. [ABSTRACT FROM AUTHOR]

In this paper we give a new proof of a result by S. Reich and A.J. Zaslavski (S. Reich and A.J. Zaslavski, A fixed point theorem for Matkowski contractions, Fixed Point Theory, 8(2007), No. 2, 303-307). Some new fixed point theorems for nonself generalized contractions are also given. [ABSTRACT FROM AUTHOR]

In this paper we study fundamental equations of holomorphically projective mappings of parabolic Kãhler spaces (which are generalized classical, pseudo- and hyperbolic Kãhler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics. [ABSTRACT FROM AUTHOR]

In this paper we will prove a fixed point theorem of Perov type for cyclic contractions on complete generalized metric spaces. Then, as an application, we will study the existence, uniqueness and approximation of the solution for a system of integral equations. [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]

In this paper we define generalized statistical convergence for sequences of sets of order α, 0 < α ⩽ 1 in sense of Wijsman and study some basic properties of this concept. [ABSTRACT FROM AUTHOR]

We are concerned with two classes of nonlinear eigenvalue problems involving equations driven by the sum of the p-Laplace (p > 2) and Laplace operators. The main results of this paper establish the existence of a continuous spectrum consisting in an unbounded interval, which is described by using the principal eigenvalue of the Laplace operator. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coefficients bounds (namely, Fekete-Szegö inequalities) for functions belonging to certain subclass of analytic functions defined by using Salagean operator. Moreover, connections of the results presented here with those obtained in earlier works are pointed out. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is introduced a new sums analogous to Dedekind sums, then using the analytic method and the properties of Dirichlet L-functions to study the arithmetical properties of this sums, and give an interesting reciprocity theorem for it. [ABSTRACT FROM AUTHOR]

In this paper we prove that there does not exist a set with more than 16 nonzero polynomials in 핂[X], where 핂 is any field of characteristic 0, such that the product of any two of them increased by a linear polynomial n ∊ 핂[X] is a square of a polynomial from 핂[X]. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the behavior of the solution of the following max type difference equation of order three xn+1 = max{An/xn,xn-2} , n = 0, 1,. . ., where the initial conditions x-2, x-1, x0 are arbitrary positive real numbers and {An}n=0∝ is a periodic sequence of period two. [ABSTRACT FROM AUTHOR]

In this paper, estimates for second and third MacLaurin coefficients of certain subclasses of bi-univalent functions in the open unit disk defined by convolution are determined, and certain special cases are also indicated. The main result extends and improve a recent one obtained by Srivastava et al. [ABSTRACT FROM AUTHOR]

In this paper, mechanical models with Newton's Law of impacts are studied. One of the most interesting properties in some of these models is chattering. This phenomenon is understood as the appearance of an infinite number of impacts occurring in a finite time. Conclusion on the presence of chattering is made exclusively by examination of the right hand side of impact models for the first time. Criteria for the sets of initial data which always lead to chattering are established. The Moon-Holmes model is subject to regular impact perturbations for the chattering generation. Using the chattering solutions, continuous chattering is generated. To depress the chattering, Pyragas control is applied. Illustrative examples are provided to demonstrate the impact chattering. [ABSTRACT FROM AUTHOR]

In this paper we have introduced the concept of geometric convergence of a sequence and determined the necessary and sufficient condition under which convergence follows from geometric convergence of a sequence in multiplicative sense. Corollaries allow this condition to be replaced by multiplicative analogues of Schmidt type slow oscillation condition or Landau type two-sided condition. [ABSTRACT FROM AUTHOR]

The Szeged index Sz(G) of a connected graph G is defined as the sum of the terms nu(e∣G)nv(e∣G) over all edges e = uv of G, where nu(e∣G) is the number of vertices of G lying closer to u than to v and nv(e∣G) is the number of vertices of G lying closer to v than to u. In this paper, some variants of the Szeged index such as the edge PI index, edge Szeged index, edge-vertex Szeged index, vertex-edge Szeged index, and revised edge Szeged index are studied under rooted product of graphs. Results are applied to compute these graph invariants for some chemical graphs by specializing components in rooted products. [ABSTRACT FROM AUTHOR]

For a positive integer k, a k-rainbow dominating function (kRDF) of a graph G is a function f from the vertex set V(G) to the set of all subsets of the set {1,2,. . .,k} such that for any vertex υ ϵ V(G) with f (υ )= ∅, the condition ∪uϵN(υ ) f ( υ ) ={1,2,. . .,k} is fulfilled, where N(υ ) is the neighborhood of v. The weight of a kRDF f is the value ω(f )= Συ ϵV∣f( υ)∣. A kRDF f is called a global k-rainbow dominating function (GkRDF) if f is also a kRDF of the complement G̅ of G. The global k-rainbow domination number of G, denoted by γgrk(G), is the minimum weight of a GkRDF on G. In this paper, we initiate the study of the global k-rainbow domination number and we establish some sharp bounds for it. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the existence of the mild solutions to the fractional impulsive evolution equations. By definitions of the lower and upper quasi-solutions and technique of mixed monotone iterative, we get several existence results. The results are new and extend previously known results. An example illustrates the main results. [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]

The concept of statistical convergence is one of the most active area of research in the field of summability. Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory and number theory. In this paper, we introduce the idea of double Jλ -statistical convergence in a locally solid Riesz space and study some of its properties by using the mathematical tools of the theory of topological vector spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove a tripled common fixed point theorem of Suzuki type for a pair of hybrid mappings in metric spaces. Our result generalizes and modifies several comparable results in the literature. We also provide an example to support our theorem. [ABSTRACT FROM AUTHOR]