a characteriation of continuity of the $p$-$lambda$-variation function is given and the helly's selection principle for $lambda bv^{(p)}$ functions is established. a characterization of the inclusion of waterman-shiba classes into classes of functions with given integral modulus of continuity is given. a useful estimate on modulus of variation of functions of class $lambda bv^{(p)}$ is found.

A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.

In the present article, we construct a new sequence of bivariate Sz?sz-Durrmeyer operators based on Dunkl analogue. We investigate order approximation with aid modulus continuity in terms well known Peetre?s K-functional, weighted results, Voronovskaja type theorems and Lipschitz maximal functions. Further, also discuss here properties B?gel-spaces by use mixed-modulus continuity.

In this paper, we establish a link between the Szász-Durrmeyer type operators and multiple Appell polynomials. We study a quantitative-Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth order central moment and Grüss-Voronovskaya type theorem. We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order mo...

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means...

In most of our work we have been concerned with the one-dimensional case, but here we shall be able to say something about the general case. Roughly speaking, our aim has been to use the finiteness of Iv,P(f) to derive a priori bounds for other important functionals of ƒ, such as its modulus of continuity or other high order norms. The bounds we have obtained involve, of course, M* and p but th...

In the present paper, we generalize Zygmund classes of functions with two variables defined by Móricz by means of modulus of continuity, and give the necessary and sufficient conditions for double sine, sine-cosine, cosinesine and double cosine series so that their sums belong to the generalized Zygmund classes. Some new results of Fülöp [1] and [2] on double trigonometric series are extended.