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In this paper, we prove the existence of infinitely many solutions for a fractional p&q-Laplacian system involving Hardy-Sobolev exponents and obtain new conclusion under different conditions. The methods used here are based on variational methods and Ljusternik- Schnirelmann theory. [ABSTRACT FROM AUTHOR]

A module M is called a UC-module if whenever every submodule of M has a unique closure. In this paper, we establish new characterizations of several well-studied classes of rings in terms of UC-modules, and show that UC is not a Morita invariant property. In addition, we study the behaviour of UC-modules under excellent extensions of rings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate eventual periodicity of the following max-type system of difference equations of higher order with four variables ... [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the existence and nonexistence of positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use the fixed point theorems on the cones in order to achieve our results. [ABSTRACT FROM AUTHOR]

T.Z. Mirkovic [14] obtained new inequalities of Wirtinger type by using some classical inequalities and special means for convex function. So in this paper, we obtain some inequalities of Wirtinger type for s-convex function, m-convex function, (α,m)-convex function, quasi-convex function and P-function. Also several special cases are discussed, which can be deduced from our main results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain sufficient conditions for existence of solutions of a third order m-point impulsive boundary value problem on time scales. To the best of our knowledge, there is hardly any work dealing with third order multi point dynamic impulsive BVPs. The reason may be the complex arguments caused by both impulsive perturbations and calculations on time scales. As an application, we give an example demonstrating our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new results on radicals of an ideal in BL-algebras. Further, we introduce I-balls in BL-algebras and prove that I-balls constitutes a basis for a topology on BL-algebras. We also derive some new relations of sequences in BL-algebras. [ABSTRACT FROM AUTHOR]

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F : X → E restricted to [c, F(c)]? is partially ideal statistically continuous at c then E is singleton. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of fuzzy barrels on locally convex fuzzy topological vector spaces. We present some characterizations of the fuzzy locally convex spaces, which are fuzzy barrelled. Using fuzzy barrels, we prove that the same fuzzy sets are bounded in any fuzzy topology of dual pair. Finally, we prove the Banach-Steinhaus theorem for the fuzzy topological vector spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some a Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a certain subclass of meromorphic multivalent close-to-convex functions. Such results as coefficient inequalities, and radius of meromorphic convexity are derived. [ABSTRACT FROM AUTHOR]

In this paper we introduce the classes Tn (p,λ,A,B) and Kn (p,λ,µ,m,A,B) and derive distortion inequalities of the functions belonging to class Kn (p,λ,µ,m,A,B). Further we apply to the (n,δ)- neighborhoods of functios in the class Kn (p,λ,µ,m,A,B). [ABSTRACT FROM AUTHOR]

The Szeged index is a modification of the Wiener index to cyclic molecules. The Szeged index of a connected graph G is defined as SZ(G)= Σe∈E(G) n1(e|G)n2(e|G), where E(G) is the edge set of G, and for any e = uν ∈ E(G), n1(e|G) is the number of vertices of G lying closer to vertex u than to vertex ν, and n2(e|G) is the number of vertices of G lying closer to vertex ν than to vertex u. In this paper, we determine the n-vertex unicyclic graphs whose vertices on the unique cycle have degree at least three with the first, the second and the third smallest as well as largest Szeged indices for n ≥ 6, n ≥ 7 and n ≥ 8, respectively. [ABSTRACT FROM AUTHOR]

The topic of rough set theory considers a relation to determine the lower and upper approximations of a set X. Originally, this relation was assumed to be an equivalence relation. This research focuses on using tolerance relations instead of equivalences, i.e. we do not assume the transitivity of the relations. More specifically, in this paper we investigate tolerances induced by irredundant coverings. We characterize the interrelation between the lattices of lower and upper approximations of such tolerances R and p. The theory of Formal Concept Analysis makes it possible to examine the inclusions of the resulting concepts. We also use quasiorders (denoted by ≤ and ≥ (p)) and an equivalence relation (denoted by ker p) for summarizing the connection between tolerances and lattices in a theorem. [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, 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 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, 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]

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]

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]

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]

Let R be a semiprime ring with center Z(R). A mapping F: R→ R is called a generalized derivation if there exists a derivation d : R→R such that F(xy) = F(x)y+xd(y) holds for all x,yϵR. In the present paper, our main object is to study the situations: (1) F(xy)-F(x)F (y)ϵ Z(R), (2) F(xy)+F(x)F(y)ϵ Z(R), (3) F(xy)-F(y)F(x) ϵ Z(R), (4) F(xy)+F(y)F(x) ϵ Z(R); for all x,y in some suitable subset of R. [ABSTRACT FROM AUTHOR]

One of the outstanding problems in combinatorial design theory is concerning the existence of 2-(v,k, 1) designs. In particular, the existence of 2-(v,k, 1) designs admitting an interesting group of automorphisms is of great interest. Thirty years ago, a six-person team classified 2-(v,k, 1) designs which have flag-transitive automorphism groups. Since then the effort has been to classify those 2-(v,k, 1) designs which are block-transitive but not flagtransitive. This paper is a contribution to this program and we prove there is nonexistence of 2-(v,k, 1) designs admitting a point-primitive block-transitive but not flag-transitive automorphism group G with socle Eg(q). [ABSTRACT FROM AUTHOR]

The paper introduces some sets of double lacunary invariant sequences defined by four dimensional RH-regular matrices and Orlicz functions. First we study some basic properties of such sets by equipping them with linear topological structure. Further, we investigate some relationships among such sets under different conditions and finally compare with a set of double lacunary statistically convergent sequences. [ABSTRACT FROM AUTHOR]

Let W = {w1;w2; … ;wk} be an ordered set of vertices of G and let v be a vertex of G. The representation r(v|W) of v with respect to W is the k-tuple (d(v,w1),d(v,w2), … ; d(v,wk)). W is called a resolving set or a locating set if every vertex of G is uniquely identified by its distances from the vertices of W, or equivalently, if distinct vertices of G have distinct representations with respect to W . A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension of G, denoted by dim(G). Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). In this paper, we study the metric dimension of barycentric subdivision of Cayley graphs Cay(Zn ⊕Zm). We prove that these subdivisions of Cayley graphs have constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of Cayley graphs Cay(Zn⊕Zm). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the multivariate Bernstein-Schurer-Stancu operators. Then, we state the Volkov-type theorem and investigate the order of convergence by means of modulus of continuity and by Lipschitz class functionals. Moreover, the inverse theorems are studied for the multivariate Stancu variant of Bernstein operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce ρ-generalized pseudo and ρ-genera-lized quasi with the tool right upper-Dini-derivative and illustrated these by non-trivial examples. Necessary and sufficient optimality conditions are obtained for a nonlinear multiobjective fractional programming problem involving some classes of generalized convexities with the tool-right upper-Dini-derivative. Furthermore, usual duality theorems are proved for a general dual problem using the concept of generalized convex functions. Our results generalize and extend the several results appeared in the literature. [ABSTRACT FROM AUTHOR]

In the present paper, two new subclasses of bi-starlike and bi-convex function of complex order associated with hypergeometric functions are introduced and coefficient estimates for functions in these classes are obtained. Several new (or known) consequences of the results are also pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we prove some properties of quasi-metric spaces and state some fixed point theorems in this setting. As applications, we show that most of recent results on G-metric spaces in [3, 10] may be also implied from certain fixed point theorems on metric spaces and quasi-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we consider cone metric type spaces which are introduced as a generalization of symmetric and metric spaces by Khamsi and Hussain in 2010. Then we prove several common fixed point for weakly compatible mappings in cone metric type spaces. All results are proved in the settings of a solid cone, without the assumption of continuity of the mappings. [ABSTRACT FROM AUTHOR]

In this paper, we consider split quaternions and split quaternion matrices. Firstly, we give some properties of split quaternions. After that we investigate split quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of split quaternion matrices and we describe some of their properties. Furthermore, we give the definition of q-determinant of split quaternion matrices. [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]

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 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 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]

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]