In this paper we extend the definition of K-positive definite operators from linear to Fréchet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems 1 and 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introdu...

In the thirties, Banach, Mazurkiewicz and Jarnnk found relations connecting Dini derivates of a typical continuous function on 0; 1] at all points of (0; 1). We prove, answering a question of K. M. Garg, that there are no further relations of this sort. An analogous result is proved also for approximate Dini derivates. The aim of this note is to present relatively simple proofs of these results...

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although Riesz–Caputo is more suitable for modeling real phenomena, there few examples literature where numerical methods solve such differential problems. In this paper, we propose approximate of a given function cubic spline. As far as aware, first time that splines have been context derivat...

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gâteaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key elem...

In this paper, we investigate the longtime behavior of time fractional reaction–diffusion equations with delay. The governing partial differential equation generalizes Hutchinson, Mackey–Glass and Nicholson’s blowflies equations. Energy estimates, asymptotic stability contractivity problem are proved. finite difference technique is used to discretize time-fractional Caputo derivative, spectral ...