On Ishikawa-type iteration with errors for a continuous real function on an arbitrary interval

2013 ◽  
Vol 7 ◽  
pp. 1901-1907
Author(s):  
Prasit Cholamjiak
Keyword(s):  
Real Function ◽  
Continuous Real Function ◽  
Arbitrary Interval

Investigating the multiplicity and concentration behaviour of solutions for a quasi-linear Choquard equation via the penalization method

2015 ◽  
Vol 146 (1) ◽  
pp. 23-58 ◽  
Author(s):  
Claudianor O. Alves ◽  
Minbo Yang
Keyword(s):  
Real Function ◽  
Local Minimum ◽  
Laplacian Operator ◽  
Positive Parameter ◽  
Choquard Equation ◽  
Primitive Function ◽  
Continuous Real Function ◽  
Penalization Method ◽  
Concentration Of Solutions ◽  
Image Position

We study the multiplicity and concentration behaviour of positive solutions for a quasi-linear Choquard equationwhere Δp is the p-Laplacian operator, 1 < p < N, V is a continuous real function on ℝN, 0 < μ < N, F(s) is the primitive function of f(s), ε is a positive parameter and * represents the convolution between two functions. The question of the existence of semiclassical solutions for the semilinear case p = 2 has recently been posed by Ambrosetti and Malchiodi. We suppose that the potential satisfies the condition introduced by del Pino and Felmer, i.e.V has a local minimum. We prove the existence, multiplicity and concentration of solutions for the equation by the penalization method and Lyusternik–Schnirelmann theory and even show novel results for the semilinear case p = 2.

Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Yunjuan Jin ◽  
Minbo Yang
Keyword(s):  
Real Function ◽  
Ground State ◽  
Elliptic Systems ◽  
Continuous Real Function ◽  
Ground State Solutions

AbstractIn this paper we consider the following Hamiltonian elliptic terns in R[XXX]Where V(x) > 0 is a periodic continuous real Function, b̅(x) = (b

scholarly journals Existência de polinômios de melhor aproximação para funções contínuas

1981 ◽  
Vol 3 (3) ◽  
pp. 13 ◽  
Author(s):  
Alcibiades Gazzoni ◽  
Alsimar T. Ferreira Gazzoni
Keyword(s):  
Polynomial Approximation ◽  
Real Function ◽  
Continuous Real Function

The paper presents the problem of monotonic approximation which consists on finding a better polynomial approximation for a continuous real function "f" defined on [a, b]. (...). The existence of polynomials of better approximation for a given function "f" was presented here.

scholarly journals On the Richter–Thomassen Conjecture about Pairwise Intersecting Closed Curves

2016 ◽  
Vol 25 (6) ◽  
pp. 941-958
Author(s):  
JÁNOS PACH ◽  
NATAN RUBIN ◽  
GÁBOR TARDOS
Keyword(s):  
Real Function ◽  
Important Ingredient ◽  
Continuous Real Function ◽  
Closed Curves ◽  
Jordan Curves ◽  
Family Of Curves ◽  
The Family ◽  
Intersection Points ◽  
Pass Through

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least (1−o(1))n2.We confirm the above conjecture in several important cases, including the case (1) when all curves are convex, and (2) when the family of curves can be partitioned into two equal classes such that each curve from the first class touches every curve from the second class. (Two closed or open curves are said to be touching if they have precisely one point in common and at this point the two curves do not properly cross.)An important ingredient of our proofs is the following statement. Let S be a family of n open curves in ℝ2, so that each curve is the graph of a continuous real function defined on ℝ, and no three of them pass through the same point. If there are nt pairs of touching curves in S, then the number of crossing points is $\Omega(nt\sqrt{\log t/\log\log t})$.

Uniform Continuity of Continuous Functions on Uniform Spaces

1961 ◽  
Vol 13 ◽  
pp. 657-663 ◽  
Author(s):  
Masahiko Atsuji
Keyword(s):  
Real Function ◽  
Metric Spaces ◽  
Uniform Space ◽  
Continuous Functions ◽  
Uniform Continuity ◽  
Uniform Structure ◽  
Uniform Spaces ◽  
Continuous Real Function ◽  
Complete Space ◽  
Uniformly Continuous

Recently several topologists have called attention to the uniform structures (in most cases, the coarsest ones) under which every continuous real function is uniformly continuous (let us call the structures the [coarsest] uc-structures), and some important results have been found which closely relate, explicitly or implicitly, to the uc-structures, such as in the vS of Hewitt (3) and in the e-complete space of Shirota (7). Under these circumstances it will be natural to pose, as Hitotumatu did (4), the problem: which are the uniform spaces with the uc-structures? In (1 ; 2), we characterized the metric spaces with such structures, and in this paper we shall give a solution to the problem in uniform spaces (§ 1), together with some of its applications to normal uniform spaces and to the products of metric spaces (§ 2). It is evident that every continuous real function on a uniform space is uniformly continuous if and only if the uniform structure of the space is finer than the uniform structure defined by all continuous real functions on the space.

scholarly journals On a nonlinear degenerate evolution equation with strong damping

1992 ◽  
Vol 15 (3) ◽  
pp. 543-552 ◽  
Author(s):  
Jorge Ferreira ◽  
Ducival Carvalho Pereira
Keyword(s):  
Weak Solution ◽  
Evolution Equation ◽  
Bounded Domain ◽  
Real Function ◽  
Smooth Boundary ◽  
Global Weak Solution ◽  
Continuous Real Function ◽  
Strong Damping ◽  
Degenerate Evolution Equation ◽  
Nonlinear Degenerate

In this paper we consider the nonlinear degenerate evolution equation with strong damping,(*)      {K(x,t)utt−Δu−Δut+F(u)=0   in   Q=Ω×]0,T[u(x,0)=u0,   (ku′)(x,0)=0   in   Ωu(x,t)=0           on   ∑=Γ×]0,T[whereKis a function withK(x,t)≥0,K(x,0)=0andFis a continuous real function satisfying(**)     sF(s)≥0,   for   all   s∈R,             Ωis a bounded domain ofRn, with smooth boundaryΓ. We prove the existence of a global weak solution for (*).

On sets of points of approximate continuity and ϱ-upper continuity

2020 ◽  
Vol 70 (2) ◽  
pp. 305-318
Author(s):  
Anna Kamińska ◽  
Katarzyna Nowakowska ◽  
Małgorzata Turowska
Keyword(s):  
Real Function ◽  
Approximate Continuity ◽  
Measurable Set ◽  
Upper Continuous ◽  
Lebesgue Measurable Set ◽  
Upper Continuity

Abstract In the paper some properties of sets of points of approximate continuity and ϱ-upper continuity are presented. We will show that for every Lebesgue measurable set E ⊂ ℝ there exists a function f : ℝ → ℝ which is approximately (ϱ-upper) continuous exactly at points from E. We also study properties of sets of points at which real function has Denjoy property. Some other related topics are discussed.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

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