Let H1 and H2 be Hilbert spaces and let B(H1,H2) be the space of bounded linear operators A : H1 → H2. An operator A ∈ B(H1,H2) is said to be Fredholm if first, the kernel ofA is finite-dimensional, and second the image ofA is closed and has finite codimension. An application of the open mapping theorem shows that the closedness requirement on the image is redundant. A well-known example of Fre...

In this paper, we define and explore the new family of exponentially convex functions which are called s–convex functions. We attain amazing examples algebraic properties newly introduced function. addition, find a novel version Hermite-Hadamard type inequality in support concept via frame classical fractional calculus (non-conformable Riemann-Liouville integrals operator). Furthermore, investi...

We introduce and study some operational quantities associated to a space ideal A. These quantities are used to define generalized semi-Fredholm operators associated to A, and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that...

Co-author: Lúıs Castro We will present a study of the Fredholm property for matrix Wiener-Hopf plus/minus Hankel operators with semi-almost periodic Fourier symbols. The Fredholm property will be described based on certain factorizations of the representatives at infinity of the original symbols, and on the geometrical mean values of the corresponding factors. The Fredholm indices of those oper...

Consider a selfadjoint unbounded operator D on a Hilbert space H and a one parameter norm continuous family of selfadjoint bounded operators {A(t) | t ∈ R} that converges in norm to asymptotes A± at ±∞. Then under certain conditions [RoSa95] that include the assumption that the operators {D(t) = D + A(t), t ∈ R} all have discrete spectrum then the spectral flow along the path {D(t)} can be show...

in this paper‎, ‎we show the stability of gustafson‎, ‎weidmann‎, ‎kato‎, ‎wolf‎, ‎schechter and browder essential spectrum of bounded linear operators on banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $u$ such $gamma(u^m)

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

In this paper, numerical solution of linear Fredholm integral equations of the second kind is considered by two methods. The methods are developed by means of the Sinc-collocation method and shifted Chebyshev polynomial method. Some numerical examples are presented to illustrate the method. Numerical solution of linear Fredholm integral equations. 1. Introduction Many initial and boundary value...

In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

Dynamical zeta functions [1], Fredholm determinants [2] and quantum Selberg zeta functions [3, 4] have recently been established as powerful tools for evaluation of classical and quantum averages in low dimensional chaotic dynamical systems [5] [8]. The convergence of cycle expansions [9] of zeta functions and Fredholm determinants depends on their analytic properties; particularly strong resul...