In this paper we introduce the sequence spaces χM (p, q, u), using an modulus function M and defined over a semi normed space (X, q), semi normed by q. We study some properties of these sequence spaces and obtain some inclusion relations.

In this paper we introduce the growth rate of χ2 defined by modulus function and study general properties of these spaces and also establish some inclusion results and duals among them..

We introduce the vector-valued sequence spaces w∞ Δ, F,Q, p, u , w1 Δ, F,Q, p, u , and w0 Δ, F,Q, p, u , S q u and S q 0u, using a sequence of modulus functions and the multiplier sequence u uk of nonzero complex numbers. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly Δuq-Cesàro summable with respect to the modulus function f then it is ...

In this paper we define the Cesàro χ2 sequence space Cesp “ χf ” defined by a modulus and exhibit some general properties of the space.

In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified estimated the convergence properties using of modulus continuity, Lipschitz- type space, Ditzian-Totik continuity. After that, weighted result also given. Finally, some results related to A-statistical o...

For minimizers u ∈W 1,p(x)(Ω) of quasiconvex integral functionals of the type F [u] := ∫ Ω f(x,Du(x)) dx with p(x) growth in the class K := {u ∈ W 1,p(x)(Ω) : u ≥ ψ}, where ψ ∈ W 1,p(x)(Ω) is a given obstacle function, we show estimates of Calderón-Zygmund type, i.e. |Dψ|p(·) ∈ L =⇒ |Du|p(·) ∈ L , for any q > 1, provided that the modulus of continuity ω of the exponent function p satisfies the ...

Let ω : [0,+∞[→ [0,+∞[ be a modulus of continuity. Consider the integral functional

We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts, that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts we prove that solutions satisfy a modulus of continuity depending only on the local L norm of the drif...

In the product space H × R, we obtain uniform a priori C horizontal length estimates, uniform a priori C boundary gradient estimates, as well as uniform modulus of continuity, for a class of horizontal minimal equations. In two independent variables, we derive a certain uniform global a priori C estimates and we infer an existence result.

The purpose of this note is to prove a central limit theorem for the L -modulus of continuity of the Brownian local time obtained in [2], using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight’s theorem and the Clark-Ocone formula for the L-modulus of the Brownian local time.