We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. AMS Mathematics Subject Classification : 45G10, 45M99, 47H09.

A proper edge-coloring of a graph G with colors 1, . . . , t is called an interval t-coloring if the colors of edges incident to any vertex of G form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, the least value of t for which G has an interval t-coloring is denoted by w(G). A graph G is ...

The design and verification of cryptographic protocols is a notoriously difficulttask, even in symbolic models which take an abstract view of cryptography. This is mainlydue to the fact that protocols may interact with an arbitrary attacker which yields averification problem that has several sources of unboundedness (size of messages, numberof sessions, etc.).In this paper, ...

The applications of software benchmarks place an obvious demand on the precision of the benchmark results. An intu­ itive and frequently employed approach to obtaining precise enough benchmark results is having the benchmark collect a large number of samples that are simply averaged or other­ wise statistically processed. We show that this approach ignores an inherent and unavoidable nondetermi...

In this short note, we establish the uniform integrability and pointwise convergence of an (unbounded) family of polynomials on the unit interval that arises in work on statistical density estimation using Bernstein polynomials. These results are proved by first establishing/generalizing some combinatorial and probability inequalities that rely on a new family of completely monotonic functions.

ÖZET Bu çalışmada, sonlu bir aralıkta verilmiş sınırsız operatör katsayılı ikinci mertebeden diferansiyel operatörün düzenli izi için bir formül bulunmuştur. Anahtar Sözcükler: Hilbert uzayı, Kendine eş operator, çekirdek operatör ABSTRACT In this work; a formula for the regularized trace of second order differential operator, which is given in a finite interval and with unbounded operator coef...

We consider a Cauchy problem for a Sturm-Liouville type differential inclusion involving a nonconvex set-valued map and we prove that the set of selections corresponding to the solutions of the problem considered is a retract of the space of integrable functions on unbounded interval.

This article concerns the asymptotic behavior of solutions one-dimensional porous medium systems with boundary degeneracy in bounded and unbounded intervals. It is shown that degree exponent nonlinear diffusion determine behaviors solutions. For problem a interval, if not strong, admits both nontrivial global blowing-up solutions, while strong enough, any solution to must blow up finite time. a...

We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker mechanisms, logarithmic market scoring rule (LMSR) and dynamic parimutuel markets (DPM), are generalized to han...

Abstract In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions’ existence for class nonlinear q-difference equations in the context Riemann–Liouville q-derivative on an infinite interval. The system’s solution formulated with help Green’s function. A compactness criterion established special space. All obtained results uniquenes...