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In the paper we study questions about solvability of some boundary value problems with periodic conditions for an inhomogeneous biharmonic equation. The exact conditions for solvability of the problems are found.

Very recently, Shahzad et al. [RACSAM 111 (2017) 307-324] introduced the notion of (A,S)- contractions which unifies several well known nonlinear type contractions (e.g. R-contractions, Z-contractions, L-contractions etc.) in one go. In this paper, we introduce the notion of generalized (A,S)f-contractions and utilize the same to present some coincidence and common fixed point results for a pair of self-mappings (g,f)defined on a metric space endowed with a binary relation S. In this course, we ought to introduce some new notions namely: (I,S)-continuity, (I,S)-compatibility and local (g,f)-transitivity. Consequently, several results involving R-contractions and Z-contractions are deduced. Finally, we furnish illustrative examples to demonstrate the utility of our results.

This paper is related to the dynamical behaviors of a discrete-time fractional-order predatorprey model. We have investigated existence of positive fixed points and parametric conditions for local asymptotic stability of positive fixed points of this model. Moreover, it is also proved that the system undergoes Flip bifurcation and Neimark-Sacker bifurcation for positive fixed point. Various chaos control strategies are implemented for controlling the chaos due to Flip and Neimark-Sacker bifurcations. Finally, numerical simulations are provided to verify theoretical results. These results of numerical simulations demonstrate chaotic behaviors over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behaviors in the model.

In this paper, we introduce the concept of extended partial b-metric space. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Then we prove some fixed point results for weakly contractive mappings in the setup of ordered extended partial b-metric spaces. An example is given to verify the effectiveness and applicability of our main results. An application of these results to Volterra-type integral equations is provided at the end.

In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [American Math. Monthly 83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015) 345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].

In this paper, we discuss and obtain some new unique common fixed point theorems for two mappings satisfying Kannan type mixed contractive conditions and Chatterjea type mixed contractive conditions respectively on cone metric spaces over Banach algebras without the assumption of normality and give some generalizations of Kannan type and Chatterjea type fixed point theorems.

S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Tur?n formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Tur?n formula that has all its nodes real and belonging to the interval of integration, [-1,1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Tur?n quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1,1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known.

In their attempt to develop domain theory in situ T0 spaces, Zhao and Ho introduced a new topology defined by irreducible sets of a resident topological space, called the SI-topology. Notably, the SI-topology of the Alexandroff topology of posets is exactly the Scott topology, and so the SI-topology can be seen as a generalisation of the Scott topology in the context of general T0 spaces. It is well known that the convergence structure that induces the Scott topology is the Scott-convergence - also known as lim-inf convergence by some authors. Till now, it is not known which convergence structure induces the SI-topology of a given T0 space. In this paper, we fill in this gap in the literature by providing a convergence structure, called the SI-convergence structure, that induces the SI-topology. Additionally, we introduce the notion of I-continuity that is closely related to the SI-convergence structure, but distinct from the existing notion of SI-continuity (introduced by Zhao and Ho earlier). For SI-continuity, we obtain here some equivalent conditions for it. Finally, we give some examples of non-Alexandroff SI-continuous spaces.

Let D be a digraph. A dominating set of D is the subset S of V(D) such that each vertex in V(D)?S is an out-neighbor of a vertex in S. The minimum cardinality of a dominating set of G is denoted by ?(D). We let D?denote the reverse of D. In [Discrete Math. 197/198 (1999) 179-183], Chartrand, Harary and Yue proved that every connected digraph D of order n ? 2 satisfies ?(D)+ ?(D?) ? 4n 3 and characterized the digraphs D attaining the equality. In this paper, we pose a reduction of the determining problem for (D)+(D?) using the total domination concept. As a corollary of such a reduction and known results, we give new bounds for (D)+(D?) and an alternative proof of Chartrand-Harary-Yue theorem.

In this paper, it is proved that a trans-Sasakian 3-manifold is locally symmetric if and only if it is locally isometric to the sphere space S3(c2), the hyperbolic space H3(-c2), the Euclidean space R3, the product space R x S2(c2) or R x H2(-c2), where c is a nonzero constant. Some examples are constructed to illustrate main results. We also give some new conditions for a compact trans-Sasakian 3-manifold to be proper.

For indicating the non-self-centrality extent of graphs, two new eccentricity-based measures namely third Zagreb eccentricity index E3(G) and non-self-centrality number N(G) of a connected graph G have recently been introduced as E3(G) = ?uv?E(G)|?G(u)-?G(v)| and N(G) = ? {u,v}?V(G) |?G(u)-?G(v)|, where ?G(u) denotes the eccentricity of a vertex u in G. In this paper, we find relation between the third Zagreb eccentricity index of graphs with some eccentricity-based invariants such as second Zagreb eccentricity index and second eccentric connectivity index. We also give sharp upper and lower bounds on the nonself-centrality number of graphs in terms of some structural parameters and relate it to two well-known eccentricity-based invariants namely total eccentricity and first Zagreb eccentricity index. Furthermore, we present exact expressions or sharp upper bounds on the third Zagreb eccentricity index and non-selfcentrality number of several graph operations such as join, disjunction, symmetric difference, lexicographic product, strong product, and generalized hierarchical product. The formulae for Cartesian product and rooted product as two important special cases of generalized hierarchical product and the formulae for corona product as a special case of rooted product are also given.

In this paper, we show some geometric conditions on Banach spaces by considering H?lder?s means and many well known parameters namely the James constant, the von Neumann-Jordan constant, the weakly convergent sequence coefficient, the normal structure coefficient, the coefficient of weak orthogonality, which imply the existence of fixed points for multivalued nonexpansive mappings and normal structure of Banach spaces. Some of our main results improve and generalize several known results in the recent literature on this topic. We also show that some of our results are sharp.

In this research a new analytical approach is used to solve nonlinear boundary value problems (BVPs) of higher order occurring in nonlinear phenomena. It converts a complex nonlinear problem into zeroth order and first order problem. It consists of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The unknown parameters are determined by minimizing the residual. Many methods which are explained in this paper are used to determine these parameters. Here Galerkin?s method is used for this purpose. It is applied to solve non-linear BVPs of fourth and fifth order. The results are compared with the already existing methods e.g., Galerkin?s Method with Quintic B-splines, Differential Transform Method (DTM), and Optimal Homotopy AsymptoticMethod (OHAM). It gives efficient and accurate first-order approximate solution. The results achieved by this technique are in excellent concurrence with the exact solution and hence proved that this method is effective and easy to apply.

Multidimensional text data contains both structured attributes and unstructured text. Unlike the traditional numerical data, it is not straightforward to apply online analytical processing on multidimensional text data. Although some OLAP methods such as topic cube have been proposed in order to effectively utilize its structured information and valuable text data, these methods cant tell the relations of topicwords. Considering that topics usually consist of several subtopics and each subtopic usually contains some topic words, we here use a topic network manner, in which related topic words are connected, to express the complex relations of topics. This paper introduces a new concept of topic network cube to perform OLAP analysis on multidimensional text databases. Firstly, we propose a method called GL-LDA based on Gibbs sampling outputs of Labeled LDA to measure the relations between topic words. Secondly, we give a storagemodel of topic network cubewhich can efficiently generate topic network using GL-LDA. Thirdly, we show how to perform OLAP analysis on topic network cube. Experimental results show that we can analyze multidimensional text databases in different granularity easily and effectively using just a few simple SQL statements, and the output network provides rich and useful information of topics.

The notions of networks and k-networks for topological spaces have played an important role in general topology. Pytkeev networks, strict Pytkeev networks and cn-networks for topological spaces are defined by T. Banakh, and S. Gabriyelyan and J. K?kol, respectively. In this paper, we discuss the relationship among certain Pytkeev networks, strict Pytkeev networks, cn-networks and k-networks in a topological space, and detect their operational properties. It is proved that every point-countable Pytkeev network for a topological space is a quasi-k-network, and every topological space with a point-countable cn-network is a meta-Lindel?f D-space, which give an affirmative answer to the following problem [25, 29]: Is every Fr?chet-Urysohn space with a pointcountable cs'-network a meta-Lindel?f space? Some mapping theorems on the spaces with certain Pytkeev networks are established and it is showed that (strict) Pytkeev networks are preserved by closed mappings and finite-to-one pseudo-open mappings, and cn-networks are preserved by pseudo-open mappings, in particular, spaces with a point-countable Pytkeev network are preserved by closed mappings.

The notion of social roles is a centerpiece of most sociological theoretical considerations. Regular equivalences were introduced by White and Reitz in [15] as the least restrictive among the most commonly used definitions of equivalence in social network analysis. In this paper we consider a generalization of this notion to a bipartite case. We define a pair of regular equivalences on a two-mode social network and we provide an algorithm for computing the greatest pair of regular equivalences.

Classes of circulant graphs play an important role in modeling interconnection networks in parallel and distributed computing. They also find applications in modeling quantum spin networks supporting the perfect state transfer. It has been noticed that unitary Cayley graphs as a class of circulant graphs possess many good properties such as small diameter, mirror symmetry, recursive structure, regularity, etc. and therefore can serve as a model for efficient interconnection networks. In this paper we go a step further and analyze some other characteristics of unitary Cayley graphs important for the modeling of a good interconnection network. We show that all unitary Cayley graphs are hamiltonian. More precisely, every unitary Cayley graph is hamiltonian-laceable (up to one exception for X6) if it is bipartite, and hamiltonianconnected if it is not. We prove this by presenting an explicit construction of hamiltonian paths on Xnm using the hamiltonian paths on Xn and Xm for gcd(n,m) = 1. Moreover, we also prove that every unitary Cayley graph is bipancyclic and every nonbipartite unitary Cayley graph is pancyclic.

In this paper, some new partially ordered Banach spaces are introduced. Based on those new partially ordered Banach spaces and applying some fixed point theorems, we present a new approach to the theory of nonlinear sequential fractional differential equations. An example illustrating our approach is also discussed.

The Wiener-type invariants of a simple connected graph G = (V(G),E(G)) can be expressed in terms of the quantities Wf = ?{u,v}?V(G) f(dG(u,v)) for various choices of the function f (x), where dG(u,v) is the distance between vertices u and v in G. In this paper, we mainly give some sufficient conditions for a connected graph to be k-connected, ?-deficient, k-hamiltonian, k-edge-hamiltonian, k-path-coverable or satisfy ?(G)? k.

In this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.

The main object of this paper is to introduce and study systematically the univalence criteria of a new family of integral operators by using a substantially general form of the widely-investigated Srivastava-Attiya operator. In particular, we derive several new sufficient conditions of univalence for this generalized Srivastava-Attiya operator. Relevant connections with other related earlier works are also pointed out.

In this paper, it is established a characterization of ?-normal coverings by means of approximation of the Cech complete paracompacta, which are the perfect preimages of completemetric spaces of weight ? ?. In particular, this characterization generalizes to an arbitrary cardinal the result of A. Garsia-Maynez [15].

The purpose of this paper is to propose and investigate a stochastic SIQR epidemic model with saturated incidence rate. Firstly, we give some conditions to guarantee the stochastic SIQR epidemic model has a unique global positive solution. Then we verify that the disease in this model will die out exponentially if Rs 0 < 1, while the disease will be persistent in the mean if Rs 0 > 1. Moreover, by constructing suitable Lyapunov functions, we establish some sufficient conditions for the existence of an ergodic stationary distribution for the model. Finally, we provide some numerical simulations to illustrate the analytical results.

In the present paper, firstly, we review the notion of the SO-complete metric spaces. This notion let us to consider some fixed point theorems for single-valued mappings in incomplete metric spaces. Secondly, as motivated by the recent work of H. Baghani et al.(A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat, 31 (2017), 3875-3884), we obtain the results of Ansari et al. [J. Fixed Point Theory Appl. (2017), 1145-1163] with very much weaker conditions. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value system for our results.

In this paper, we obtain subordination, superordination and sandwich-type results regarding to certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also, an application of the subordination and superordination theorems to the Gauss hypergeometric function are considered. These new results generalize some previously well-known sandwich-type theorems.

In this paper, we extend the proximal point algorithm proposed by Chang et al.[8] for total asymptotically nonexpansive mapping in CAT(0) spaces. We also demonstrate the ?-convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the Ces?ro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces.

In this paper, we define the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind. Then we give the exponential, combinatorial, permanental and determinantal representations and the Binet formulas of the adjacency-Jacobsthal-Hurwitz numbers of the first and second kind by the aid of the generating functions and the generating matrices of the sequences defined.

In this paper we present a modification of the Phillips operators which reproduces the functions eat, ebt, a,b ? R. We study the moments and basic approximation properties for these new operators. For this purpose we adapt several already known result to the particular features of the new sequence that we propose here.

This paper is devoted to study the existence of solutions for a class of variational-hemivariationallike inequalities in reflexive Banach spaces. Using the notion of the stable (?,?)-quasimonotonicity, the properties of Clarke?s generalized directional derivative and Clarke?s generalized gradient, we establish some existence results of solutions when the constrained set is nonempty, bounded (or unbounded), closed and convex. Moreover, a sufficient condition to the boundedness of the solution set and a necessary and sufficient condition to the existence of solutions are also derived.

In this paper, by using some families of special numbers and polynomials with their generating functions and functional equations, we derive many new identities and relations related to these numbers and polynomials. These results are associated with well-known numbers and polynomials such as Euler numbers, Stirling numbers of the second kind, central factorial numbers and array polynomials. Furthermore, by using higher-order partial differential equations, we derive some combinatorial sums and identities. Finally, we give two computation algorithms for Euler numbers and central factorial numbers.

In this paper, a boundary analysis is carried out for the derivative of driving point impedance functions, which is mainly used for synthesis of networks containing RL, RC and RLC circuits. It is known that driving point impedance function, Z(s), is an analytic function defined on the right half of the s-plane. In this study, we derive inequalities for the modulus of derivative of driving point impedance function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and the sharpness of these inequalities is proved. Furthermore, an equation for the driving point impedance function, Z(s), is obtained as a natural result of the proved theorem in this study.

In this paper, we give generalizations of Jensen?s, Jensen-Steffensen?s and converse of Jensen?s inequalities by using generalized majorization inequalities. We also present Gr?ss and Ostrowski-type inequalities for the generalized inequalities.

In this paper, categorical properties of L-fuzzifying convergence spaces are investigated. It is shown that (1) the category L-FYC of L-fuzzifying convergence spaces is a strong topological universe; (2) the category L-FYKC of L-fuzzifying Kent convergence spaces, as a bireflective and bicoreflective subcategory of L-FYC, is also a strong topological universe; (3) the category L-FYLC of L-fuzzifying limit spaces, as a bireflective subcategory of L-FYKC, is a topological universe.

In this paper, using the fixed point method, we prove some results related to the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random C*-algebras and non-Archimedean random Lie C*-algebras for the generalized additive functional equation ?1 ? i < j ?n f(xi+xj/2 + ?n-2 l=1,kl?i,j xkl) = (n-1)2/2 ?n,i=1 f(xi) where n ? N is a fixed integer with n ? 3.

In this paper, an iterative method is applied to solve some p-Laplacian boundary value problem involving Riemann-Liouville fractional derivative operator. More precisely, we establish the existence of two positive solutions. Moreover, we prove that these solutions are one maximal and the other is minimal. An example is presented to illustrate our main result. Finally, a numerical method to solve this problem is given.

In this paper, we present a unified approach to the study of shift-invariant systems to be frames on local fields of positive characteristic. We establish a necessary condition and three sufficient conditions under which the shift-invariant systems on local fields constitute frames for L2(K). As an application of these results, we obtain some known conclusions about the Gabor frames and wavelet frames on local fields.

In this paper, we consider a generalized (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera- Sawada (CDGKS) equation. By using the Bell polynomial, we derive its bilinear form. Based on the homoclinic breather limit method, we construct the homoclinic breather wave and the rational rogue wave solutions of the equation. Then by using its bilinear form, some solitary wave solutions of the CDGKS equation are provided by a very natural way. Moreover, some prominent characteristics for the dynamic behaviors of these solitons are analyzed by several graphics. Our results show that the breather wave can be transformed into rogue wave under the extreme behavior.

In this paper we study radicals of a semigroup which is the union of a family of its subsets, indexed by a nonempty set, such that the intersection of two distinct subsets is contained in the set of left zeroes of that semigroup.

In this paper, we investigate the notion of analytic core and quasi-nilpotent part of a linear relation. Furthermore, we are interested in studying the set of Generalized Kato linear relations to give some of their properties in connection with the analytic core and the quasi-nilpotent part. We finish by giving a perturbation result for this set of linear relations.

In this paper, we prove the inequality between the generalized normalized ?-Casorati curvatures and the normalized scalar curvature for the bi-slant submanifolds in T-space forms and consider the equality case of the inequality. We also develop same results for semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds, slant submanifolds, invariant and anti-invariant submanifolds in T-space forms.

A 2-rainbow dominating function (2RDF) of a graph G is a function f : V(G) ? P({1,2}) such that for each v ? V(G) with f (v) = ? we have Uu?N(v) f (u) = {1,2}. For a 2RDF f of a graph G, the weight w(f) of f is defined as w(f)=?v?V(G)?f(v)?. The minimum weight over all 2RDFs of G is called the 2-rainbow domination number of G, which is denoted by ?r2(G). A subset S of vertices of a graph G without isolated vertices, is a total dominating set of G if every vertex in V(G) has a neighbor in S. The total domination number ?t(G) is the minimum cardinality of a total dominating set of G. Chellali, Haynes and Hedetniemi conjectured that ?t(G)? ?r2(G) [M. Chellali, T.W. Haynes and S.T. Hedetniemi, Bounds on weak Roman and 2-rainbow domination numbers, Discrete Appl. Math. 178 (2014), 27-32.], and later Furuya confirmed the conjecture [M. Furuya, A note on total domination and 2-rainbow domination in graphs, Discrete Appl. Math. 184 (2015), 229-230.]. In this paper, we provide a constructive characterization of trees T with ?r2(T) = ?t(T).

Let T be a bounded linear operator on a complex Hilbert space and n,m ? N. Then T is said to be n-normal if T+Tn = TnT+ and (n,m)-normal if T+mTn = TnT+m. In this paper, we study several properties of n-normal, (n,m)-normal operators. In particular, we prove that if T is 2-normal with ?(T) ? (-?(T)) ? {0}, then T is polarloid. Moreover, we study subscalarity of n-normal operators. Also, we prove that if T is (n,m)-normal, then T is decomposable and Weyl?s theorem holds for f (T), where f is an analytic function on ?(T) which is not constant on each of the components of its domain.

In this article, the complete convergence for weighted sums of widely orthant dependent (WOD, in short) random variables without identical distribution is investigated. In addition, the complete moment convergence for weighted sums of WOD random variables is also obtained. The results obtained in the paper generalize some corresponding ones for some dependent random variables.

Schuster introduced the notion of radial Blaschke-Minkowski homomorphism and considered its Busemann-Petty problem. In this paper, we further study the Busemann-Petty problem for the radial Blaschke-Minkowski homomorphisms and give the affirmative and negative forms of Busemann-Petty problem for the i-th radial Blaschke-Minkowski homomorphisms.

In this paper, weobtained best proximity coincidence point theorems for ?-Geraghty contractions in the setting of complete metric spaces by using weak P-property. Also we presented some examples to prove the validity of our results. Our results extended and unify many existing results in the literature. Moreover, in the last section as applications of our main results, we can apply some coincidence best proximity point and coupled coincidence proximity point on metric spaces endowed with an arbitrary binary relation.

The present paper is concerned with the solution of the coupled generalized Sylvester-transpose matrix equations {A1XB1 + C1XD1 + E1XTF1 = M1, A2XB2 + C2XD2 + E2XTF2 = M2, including the well-known Lyapunov and Sylvester matrix equations. Based on a variant of biconjugate residual (BCR) algorithm, we construct and analyze an efficient algorithm to find the (least Frobenius norm) solution of the general Sylvester-transpose matrix equations within a finite number of iterations in the absence of round-off errors. Two numerical examples are given to examine the performance of the constructed algorithm.

The aim of the current paper is introducing a generalization of Darbo?s fixed point theorem based on SR-functions. In comparison with simulation function, SR-functions are able to cover the Meir-Keeler functions. Thus, the integral equations which are related to L-functions can be solved by our results. In the sequel, we find a solution for an integral equation to support our results.

For a bounded linear operator T on a complex Hilbert space and n ? N, T is said to be n-normal if T*Tn = TnT*. In this paper we show that if T is a 2-normal operator and satisfies ?(T) ? (-?(T)) ? {0}, then T is isoloid and ?(T) = ?a(T). Under the same assumption, we show that if z and w are distinct eigenvalues of T, then ker(T-z)? ker(T-w). And if non-zero number z ? C is an isolated point of ?(T), then we show that ker(T-z) is a reducing subspace for T. We show that if T is a 2-normal operator satisfying ?(T) ?(-?(T)) = 0, then Weyl?s theorem holds for T. Similarly, we show spectral properties of n-normal operators under similar assumption. Finally, we introduce (n,m)-normal operators and show some properties of this kind of operators.

In this paper, we introduce a new algorithm for solving the split equality common null point problem and the equality fixed point problem for an infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach spaces. We then apply this algorithm to the equality equilibrium problem and the split equality optimization problem. In this way, we improve and generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et al [11], and Sitthithakerngkiet et al [21].

In this paper,we continue the study of finite sum of weighted composition operators between different Lp-spaces that was investigated by Jabbarzadeh and Estaremi in 2012. Indeed, we first obtain some necessary and sufficient conditions for boundedness of the finite sums of weighted composition operators between distinct Lp-spaces. In the sequel, we investigate the compactness of finite sum of weighted composition operators. By using theorems of boundedness and compactness, we estimate the essential norms of these operators. Finally, some examples to illustrate the main results are given.