In this article, we introduce the notions of deferred Euler statistical convergence with respect to power series as well as g-deferred Euler statistical convergence in the sense of power series method for double sequences of real numbers. Furthermore, we establish applications of these convergences in the form of a Korovkin-type approximation theorem. Finally, we determine the rate of convergence.
In this paper, we show that every rough Wijsman convergent nested sequence of sets is rough Hausdorff convergent to the same set. In addition, we characterize the rough Hausdorff limit and rough Wijsman limit of a sequence by using the unions and intersections of the r-enlargement terms of this sequence.
In this paper, the helices and polynomial curves of constant breadth are investigated using the Frenet-like curve frame in Euclidean 3-space. It is shown that in some exceptional cases, the polynomial space curves of constant breadth are helices. Moreover, the differential equations characterizing the polynomial space curves of constant breadth in Euclidean 3-space are presented.
In this paper, we investigate the tricolorability of alternating potholder diagrams APn, a class of knot diagrams constructed over the potholder curve Pn. Tricolorability is a combinatorial property used to distinguish different knot types by assigning three colors to the strands of a knot diagram under specific rules. We identify which alternating potholder diagrams are tricolorable.
In this article, using the q-calculus, the resolvent of the qSturm-Lioville operator under impulsive boundary conditions is discussed. In this context, the historical development of the subject is discussed in the introduction. In the Preliminaries section, the basic concepts of qcalculus are given, i.e., q-derivative and q-integral definitions are given, and a Hilbert space for impulsive q-Sturm-Liouville problems is defined. In the main results section, Green's function corresponding to the impulsive q-Sturm-Liouville problem is established. With the help of Green's function, the resolvent operator for the impulsive q-Sturm-Liouville problem is defined. The compactness of the resolvent operator corresponding to the impulsive q-Sturm-Liouville problem is obtained by showing that this function is a Hilbert-Schmidth kernel. The spectral function corresponding to the impulsive q-Sturm-Liouville operator is generated. Using the spectral function, the integral representation of the resolvent operator of the impulsive q-Sturm-Liouville operator in the singular case is obtained.
