In this paper, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for certain matrix operators on the Fibonacci difference sequence spaces `p(F̂ ) and `∞(F̂ ) to be compact, where 1 ≤ p <∞.

We present a survey of the theory measures noncompactness and discuss some fixed point theorems Darbo’s type. apply technique to characterization classes compact operators between certain sequence spaces, in solving infinite systems integral equations spaces. also recent results related existence best proximity points (pairs) for cyclic noncyclic condensing Banach spaces equipped with suitable ...

We study the existence and stability of solutions for a class of nonlinear functional evolution inclusions involving accretive operators. Our approach is employing the fixed point theory for multivalued maps and using estimates via the Hausdorff measure of noncompactness.

In this paper, we study the existence of mild solutions for quasilinear integrodifferential equations with nonlocal conditions in Banach spaces. The results are established by using Hausdorff’s measure of noncompactness.

We fill the gap in understanding the relationship between mappings which are condensing w.r.t. the measure of noncompactness defined on the hyperspace and multifunctions condensing in the ordinary sense.

We prove two existence theorems for the integrodifferential equation of mixed type: x′(t) = f (t,x(t), t0k1(t,s)g(s,x(s))ds, ∫ a 0k2(t,s)h(s,x(s))ds), x(0) = x0, where in the first part of this paper f , g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f , g, h, x are weakly-weakly sequentially continuous fu...

We have introduced a new sequence space l(r,s,t, p;Δ(m) ) combining by using generalized means and difference operator of order m . Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the α -, β -, γ duals of this space are computed and also obtained necessary and sufficient conditions for s...