Revistas académicas de la Universidad Católica del Norte
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Connected edge monophonic number of a graph
No full textFor a connected graph G of order n,a set S of vertices is called an edge monophonic set of G if every edge of G lies on a monophonic path joining some pair of vertices in S, and the edge monophonic number me(G) is the minimum cardinality of an edge monophonic set. An edge monophonic set S of G is a connected edge mono-phonic set if the subgraph induced by S is connected, and the connected edge monophonic number mce(G) is the minimum cardinality of a connected edge monophonic set of G. Graphs of order n with connected edge monophonic number 2, 3 or n are characterized. It is proved that there is no non-complete graph G of order n > 3 with me(G) = 3 and mce(G) = 3. It is shown that for integers k,l and n with 4 < k < l < n, there exists a connected graph G of order n such that me(G) = k and mce(G) = l.Also, for integers j,k and l with 4 < j < k < l, there exists a connected graph G such that me(G)= j,mce(G)= k and gce(G) = l,where gce(G) is the connected edge geodetic number ofa graph G
An approximation formula for n!
No full textWe prove the following very accurate approximation formula for the factorial function:n!p ???-???(? + 1 + 72(3(¾¾¾!+!)2332800 - (^ +1? This gives better results than the following approximation formula, at- n -n I 1 1 31 139 9871?! Pá V27rnne n\ n +---1--------H---,V 6 72n 6480n2 155520?3 6531840?4'which is established by the author [5] and C. Mortici [16] independently, and gives similar results with32 32 ? n 176 128, r- (?\n 8/???? 32176 ~? ?! Pá ?/? — \ 16?4 + — ?3 + — ?2 + —— ? Ve/ V 3 9 4053 9 405 1215which is established by C. Mortici in his very new paper [8]
Edge Detour Monophonic Number of a Graph
No full textFor a connected graph G of order at least two, an edge detour monophonic set of G is a set S of vertices such that every edge of G lies on a detour monophonic path joining some pair of vertices in S. The edge detour monophonic number of G is the minimum cardinality of its edge detour monophonic sets and is denoted by edm(G) .We determine bounds for it and characterize graphs which realize these bounds. Also, certain general properties satisfied by an edge detour monophonic set are studied. It is shown that for positive integers a, b and c with 2 < a < b < c, there exists a connected graph G such that m(G) = a, m!(G) = b and edm(G) = c,where m(G) is the monophonic number and m! (G) is the edge monophonic number of G. Also, for any integers a and b with 2 < a < b, there exists a connected graph G such that dm(G) = a and edm(G)= b,where dm(G) is the detour monophonic number of a graph G
Some new generalized I-convergent difference sequence spaces defined by a sequence of moduli
No full textIn this article we introduce the sequencespace cI0(F,p, ∆nv) and lI∞ (F,p, ∆nv) for the of sequence of modulii F = (/¾) and given some inclusion relations. These results here proved are analogus to those by M.Aiyub [1](Global Journal of Science Frontier Research Mathematics and Decision Sciences 12(9)(2012),32-36
Generalized Ulam—Hyers—Rassias stability of a Cauchy type functional equation
No full textUsing the alternative fixed point theorem, we establish the generalized Hyers—Ulam—Rassias stability of a Cauchy type functional equationfor functions takin values in arbitrary complete (real or complex)β-normed spaces
Banach's and Kannan's fixed point results in fuzzy 2-metric spaces
No full textIn this paper we establish two common fixed point theorems in fuzzy 2-metric spaces. These theorems are generalizations of the Banach Contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy 2-metric spaces
Uniform Convergence in B-Duals
No full textLet E be a vector valued sequence space with â-dual Åâã. We consider sufficient conditions on E for the series in a pointwise bounded subset of Åâã to be uniformly convergent over certain subsets of E. The conditions involve gliding hump assumptions on the multiplier space E. Applications to matrix mappings between vector valued sequence spaces are given
Lacunary generalized difference statistical convergence in random 2-normed spaces
No full textRecently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary An-statistical convergence and lacunary An-statistical Cauchy sequences in random 2-normed spaces using la-cunary density and prove some interesting theorems
Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with variable delay
No full textIn this article we study the existence of positive periodic solutions for two types of second-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnosel-skii's fixedpoint theoremdealing withasum of twomappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Cheung, Ren and Han 7
Asymptotics for Klein—Gordon equation
No full textWe propose a simple method for constructing an asymptotic of an eigenvalue for the Klein—Gordon equation in the presence of a shallow potential well, reducing the initial problem to an integral equation and then by applying the method of Neumann series to solve it