We consider the second-order nonlinear difference equations of the form ∆(rn−1∆xn−1) + pn f (xn−k) = hn. We show that there exists a solution (xn), which possesses the asymptotic behaviour ‖xn − a ∑n−1 j=0 (1/r j) + b‖ = o(1), a,b ∈ R. In this paper, we extend the results of Agarwal (1992), Dawidowski et al. (2001), Drozdowicz and Popenda (1987), M. Migda (2001), and M. Migda and J. Migda (1988...

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from space $ \left\vert \overline N_p^{\phi }\right\vert _{k}$, all series summable by absolute weighted mean summability method, to one classical sequence spaces $c_{0},c,l_{\infty }.$ Also, obtain necessary and sufficient conditions for each in these classes be compact establish a number ...

A long-standing question in the theory of measures noncompactness is that for Kuratowski measure α defined on a metric space M, and every bounded subset B⊂M, there countable B0⊂B such α(B0)=α(B)? In this paper, we give an affirmative answer to above. It done by showing each nonempty set B Banach space, so strongly finitely representable B0, free ultrafilter U affinely isometric ultrapower [co(B...

In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking these inclusions that defined, continuous, and bounded on semi-infinite interval. Our proof is based technique associated measures noncompactness by given modulus continuity in space BC(R+). addition, some sufficient conditions investigated to demonstr...

Abstract The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated this article. Initially, a system proposed the existence mild solution for established using Mönch fixed-point theorem contemplating Hausdorff measures noncompactness. Then, stability results i...

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

Sufficient conditions for the controllability of nonlinear neutral Volterra integrodifferential systems with implicit derivative are established. The results are a generalisation of the previous results, through the notions of condensing map and measure of noncompactness of a set.