Abstract. We prove that for every function f : X → Y , where X is a separable Banach space and Y is a Banach space with RNP, there exists a set A ∈ Ã such that f is Gâteaux differentiable at all x ∈ S(f) \ A, where S(f) is the set of points where f is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every K-monotone function on a separable Banach space is...

Bilgisayar teknolojilerindeki gelişmeler zor ve karmaşık hesaplamalar içeren kesirli matematik alanına olan ilgiyi arttırmıştır. Özellikle, gerçek sistemleri modellemedeki başarısı nedeniyle kontrol alanında çokça yararlanılmaktadır. Pek çok çalışma yapılmasına rağmen matematiği literatürde hala çözümsüz durumlar bulunmaktadır. Kontrol kullanımında karşılaşılan en büyük zorluk analitik çözüm ek...

Abstract In this work the Monte Carlo method, introduced recently by authors for orders of differentiation between zero and one, is further extended to higher than one. Two approaches have been developed on way. The first approach based interpreting coefficients Grünwald–Letnikov fractional differences as so called signed probabilities, which in case one can be negative or positive. We demonstr...

Singular source terms in sub-diffusion equations may lead to the unboundedness of solutions, which will bring a severe reduction convergence order existing time-stepping schemes. In this work, we propose two efficient schemes for solving with class mildly singular time. One discretization is based on Grünwald-Letnikov and backward Euler methods. First-order error estimate respect time rigorousl...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

The relationships between the generalized directional derivative of the distance function and the existence of nearest points as well as some geometry properties in Banach spaces are studied. It is proved in the present paper that the condition that for each closed subset G of X and x ∈ X \ G, the Clarke, Michel-Penot, Dini or modified Dini directional derivative of the distance function is 1 o...

It is proved that the class of operator equations F(y) = f solvable by a DSM (dynamical systems method) Newton-type method, u̇ = −[F (u) + a(t)I]−1[Fu(t) + a(t)u − f ], u(0) = u0, (∗) is large. Here F : X → X is a continuously Fréchet differentiable operator in a Banach space X , a(t) : [0, ∞) → C is a function, limt→∞ |a(t)| = 0, and there exists a y ∈ X such that F(y) = f . Under weak assumpti...

A new characterization of bivariate copulas is given by using the notion of Dini derivatives. Several examples illustrate the usefulness of this result.

In this paper, we show that higher-order optimality conditions can be obtain for arbitrary nonsmooth function. We introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper extended real function. This derivative is consistent with the classical higher-order Fréchet directional derivative in the sense that both derivatives of the same...