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In this paper we are addressing a counting problem of discrete mathematics, more precisely of digital geometry. In the Euclidean plane the shortest path between any two points is given by the straight line segment connecting the points. In discrete mathematics, the shortest path is usually not unique, e.g., in graphs there could be several shortest paths between two vertices. In this paper, a special infinite graph, the square grid, (i.e., the usual digital plane) is used. In digital geometry there are various digital, i.e., path based distance functions. A neighborhood sequence B gives the condition for each step of a B-path separately what type of neighborhood is used in that step. Therefore, the length and also the number of the shortest paths between two points depend not only on the respective positions (coordinate differences) of the points but also on the neighborhood sequence B. We give an algorithm and also closed formulae to compute the number of shortest B-paths. [ABSTRACT FROM AUTHOR]

In this paper the Decomposition Theorem for functional equations is shown. As an application of this Theorem the two times continuously differentiable solution of the functional equation G1(x(x+y))+F1(y) = G2(y(x+y))+F2(y) can be given with unknown functions ... where the Equation is fulfilled for all ... . [ABSTRACT FROM AUTHOR]

The problem of identifying of the several unknown time dependent parameters in the minor coefficient and in the special type right-hand side function of the semilinear higher order ultraparabolic equation from the additional initial, boundary and integral type overdetermination conditions is considered in this paper. The sufficient conditions of the unique solvability on the interval [0;T]; where T is determined by the coefficients of the equation, are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of an admissible extended Z-contraction mapping in the setting of extended b-metric spaces. As an application, we consider Ulam stability problems based on our contractions. The presented results cover several existing results in the literature. [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 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 obtain some new integral inequalities like Hermite-Hadamard type for log-convex functions and P-functions. [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]

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, 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]

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]

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, 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 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]

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]

In this paper, we introduce and investigate a new subclass HΣh,p (λ;O) of analytic and bi-univalent functions in the open unit disk U: For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. [ABSTRACT FROM AUTHOR]

Let D be a finite and simple digraph with vertex set V(D). A twin Roman dominating function (TRDF) on D is a labeling f W V(D) → {0,1,2}g such that every vertex with label 0 has an in-neighbor and out-neighbor with label 2. The weight of a TRDF f is the value w(f)= ΣvεV(D) f (v). The twin Roman domination number of a digraph D, denoted by γR(D), equals the minimum weight of a TRDF on D. In this paper we initiate the study of the twin Roman domination number in digraphs. In particular, we present sharp bounds for γR(D) and determine the exact value of the twin Roman domination number for some classes of digraphs. [ABSTRACT FROM AUTHOR]

In this paper, we study Baskakov type positive operators in polynomial weighted spaces of functions of two variables. We obtain some well known operators by using our operators which are special cases of them. We give theorems on approximation, on the degrees of approximations of functions and the Vornovskaya type theorem for these operators. Finally, we present an open problem concerning the q analogue of these 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 provide sharp bounds for the Jensen divergence generated by different classes of functions including functions of bounded variation, absolutely continuous, Lipschitz continuous, convex functions and differentiable functions whose derivatives enjoy various properties as mentioned above. The bounds are expressed in terms of known and simpler divergence measures that are of importance in various applications such as the analysis of diversity as between and within populations and to cluster analysis. [ABSTRACT FROM AUTHOR]

In this paper we investigate the boundedness of the Gerber-Shiu expected discounted penalty function applied in insurance mathematics. We give a necessary and sufficient condition for its boundedness. This condition is essentially the boundedness of the conditional expectation given the ruin occurs at the first claim. It assures that the integral equation satisfied by the Gerber- Shiu function has a unique bounded solution and it is exactly the Gerber-Shiu function. By the help of the proven necessary and sufficient condition we can also simplify the theorem concerning the necessary and sufficient condition for the limit property. We do not assume independence between the inter-claim time and the claim size but the results can be applied to the usually investigated independent case as well. We present examples to show the applicability of the condition. [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, 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]

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]