in the present article, we propose the $(p,q)$variant of genuine baskakov durrmeyer operators. we obtain moments and establish some directresults, which include weighted approximation and results in terms of modulus of continuity of second order.

This paper is devoted to the investigation of weighted mean topological dimension in dynamical systems. We show that not larger than metric dimension, which generalizes classical result Lindenstrauss and Weiss [16] . also establish relationship between entropy systems, indicates each system with finite or small boundary property has zero dimension.

‎In this paper‎, ‎we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces‎, ‎not necessarily compact‎. ‎We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators‎. ‎We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.