Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous The present authors continued study on by utilizing concept gpα-closed sets topology and introduced weakly, subweakly almost functions. Further, properties these established.

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.

In this paper, we investigate inhomogeneous and simultaneous Diophantine approximation in beta dynamical systems. For $\beta>1$ let $T_{\beta}$ be the $\beta$-transformation on $[0,1]$. We determine Lebesgue measure Hausdorff dimension of set \[\left\{(x,y)\in [0,1]^2: |T_{\beta}^nx-f(x,y)|<\varphi(n)\text{ for infinitely many }n\in\mathbb{N}\right\},\] where $f:[0,1]^2\to [0,1]$ is a Lipschitz...