Further aspects of I K-convergence in topological spaces

In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.

A NEW GENERALIZATION OF M-METRIC SPACE WITH SOME FIXED POINT THEOREMS

In this paper, we introduce a new sequential space as a generalization of M − metricspaces and M b − metric spaces. In this generalized space we define two contractive mappings namely m − contraction and m − quasi-contraction and prove some fixed point theorems for such type of mappings. Several illustrative examples have been presented in strengthening the hypothesis of our theorems.

Sequential space fractional diffusion equation’s solutions via new inner product

In this study, we determine the analytic solutions of sequential space fractional differential equations with Dirichlet boundary conditions and initial conditions in one dimension. We constructed a Fourier series solution for the eigenfunctions of a corresponding Sturm–Liouville eigenvalue problem, including fractional derivative in Caputo sense using the separation of variables. We defined a new inner product with a weighted function to get coefficients in the Fourier series.

Recognizability of Tetrahedral Picture Languages

In two dimensions, tiling the plane plays a vital role. Many picture generative models were attempted to tile the three dimensional space. A. Dharani et al. [6] introduced a new theoretical picture generative model to tile a three dimensional space using tetrahedral tile in two different ways namely Sequential Space Filling Grammar (SSFG) and Parallel Space Filling Grammar (PSFG). Local and recognizable tetrahedral picture languages are introduced in this paper and some of its properties are studied.