In this work, we find upper and lower bounds on the maximum fractional forcing number of the Cartesian power of even cycles. Our result can extend the result of [3] about the maximum forcing number of $C_{2n}\square C_{2n}$ to that of the product of an arbitrary number of even cycles of the same lengths.

Let $ℝ$ be the field of real numbers and ${ℝ}^n$ be the $n$-dimensional vector space over $ℝ$, where . Let $X$ be a Tyhonoff topological space and assume that it has at least two elements. For natural actions on ${ℝ}^n$ of the group of all non-degenerate linear transformations, the group of all affine transformations and their some subgroups, problems of equivalence of topological immersions of $X$ in ${ℝ}^n$ are investigated. Complete systems of global invariants of a topological immersion of $X$ in the space ${ℝ}^n$ are obtained for these groups. Complete systems of relations between elements of the complete systems of invariants are investigated.

In this paper we prove the two-weight boundedness of Riesz potential and its commutators on weighted global Morrey-type spaces $G{ℳ}_{\omega }^{p,\theta ,\phi }({ℝ}^n)$. Also we give some applications of our results.

In this work, we introduce and investigate a new class $k-\tilde{U}{S}_s^m(\lambda ,\gamma ,t)$ of analytic functions in the open unit disc $U$ with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions $f$ belonging to this class.

In this work, we consider a logarithmic Lamé system with distributed delay term. Firstly, we study the well-posedness of solutions by using the semigroup theory. Then, we prove the solution of the Lamé system is uniformly bounded and global in time. Finally, we prove the decay of the solution. Our results are more general than the earlier results.

The main purpose of this paper is to introduce the concepts of Wijsman $C_{\lambda }$-statistical convergence, Wijsman $C_{\lambda }$-summability and Wijsman $ℐ$-$C_{\lambda }$-summability for sequence of sets by using Cesàro submethod. Also, we establish some relations among the Wijsman $C_{\lambda }$-summability, Wijsman $D_{\lambda }$-summability and Wijsman $C_1$-summability. Finally, we have given some equivalence results for these concepts.

The notion of capability for pairs of groups was defined by Ellis in 1996. Also, the concept of capability of Lie algebras was introduced by some authors, and is analogous to the group case. In this paper, we generalize the concept of capability of a Lie algebra $L$ to the polynilpotent capability of a pair $(N,L)$ of Lie algebras and introduce a criterion for polynilpotent capability of $(N,L)$.

This paper includes a new three stage iterative method $\mathcal{A}{ℳ}^{*}$ and uses that method to test some convergence theorems in Banach spaces, together with the example to prove efficiency of $\mathcal{A}{ℳ}^{*}$ is the central focus of this paper, along with explaining, using an example, that $\mathcal{A}{ℳ}^{*}$ is converging to an invariant point faster than all Picards, Mann, Ishikawa, Noor, SP, S, Picard-S, Garodia, $K$ and $K^{*}$. It must be noted that it is also addressed by the $\mathcal{A}{ℳ}^{*}$ iterative method, the effects of stability and data dependency on contraction mapping. In addition, the $\mathcal{A}{ℳ}^{*}$ iterative method can be used to resolve differential equations with a time-delayed argument.

In this paper, we consider Klein-Gordon s-wave equation with boundary conditions polynomially dependent on the spectral parameter. We have obtained the uniqueness of the solution to the inverse problem of scattering theory on the semiaxis for the boundary value problem.