The well established theory of summability of simple series has been brought to a high degree of development; however the extension of this theory to multiple series is still in its infancy. As regards to the double series, in the proposed paper a result on absolute indexed matrix summability with an additional parameter of doubly infinite lower triangular matrix has been established that generalizes a theorem of E. Savaş and B. E. Rhoades [10] (see E. Savaş and B. E. Rhoades, Double absolute summability factor theorems and applications, Nonlinear Anal. 69 (2008), 189-200). Furthermore, some concluding remarks and applications are presented in support of our result.

Firstly, a generalization of Riemannian submersions, slant submersions and semi-slant submersions, we introduce semi-slant Riemannian maps from almost contact metric manifolds onto Riemannian manifolds. In this paper, we obtain some results on such maps by taking the vertical structure vector field. Among them, we study integrability of distributions and the geometry of foliations. Further, we find the necessary and sufficient conditions for semi-slant Riemannian maps to be harmonic and totally geodesic. We, also investigate some decomposition theorems and provide some examples to show the existence of the maps.

Adopting the so-called concavity method, we establish a finite time blow-up result for a class of fourth-order non-linear wave equations with positive energy.

Recently many published works made on local function used in ideal topological spaces can be found in related literature. "Semi Local Functions in Ideal Topological Spaces", "Closure Local Functions", and "$()^p$ and $\psi_p$-Operator" can be mentioned among such works those aim to define such functions. In general, the researchers prefer using the generalized open sets instead of topology in ideal topological spaces. Obtaining a Kuratowski closure operator with the help of local functions is an important detail in ideal topological space. However, it is not possible to obtain a Kuratowski closure operator from many of these local functions proposed by the above mentioned works. In order to address the lack of such an operator, the goal of this paper is to introduce another local function to give possibility of obtaining a Kuratowski closure operator. On the other hand, regular local functions defined for ideal topological spaces have not been found in the current literature. Regular local functions for the ideal topological spaces has been described within this work. Moreover, with the help of regular local functions Kuratowski closure operators $cl_I^{*r}$ and $\tau^{*r}$ topology are obtained. Many theorems in the literature have been revised according to the definition of regular local functions.

The purpose of this work is to give modified definitions of Apostol-Euler polynomials and numbers of higher order. We establish their elementary properties, sums, explicit relations, integrals and differential relations. A number of new results which introduced are generalization of known results and their special cases lead to the corresponding formulas of the classical Euler numbers and polynomials.

In this paper, using the idea of weighted sharing we investigate the uniqueness problem of a meromorphic function and an $L$-function when certain differential polynomials generated by them share a nonzero finite value or have the same fixed points. Our results improve the recent results due to Liu-Li-Yi [Proc. Japan Acad. Ser. A, 93 (2017), 41-46].

In this paper, we give some approximation properties by Stancu-Kantorovich operators based on inverse Pólya-Eggenberger distribution in the polynomial weighted space introduced in the literature and obtain convergence properties of these operators by using Korovkin's theorem. We discuss the direct result and Voronovskaja type asymptotic formula.

The main objective of this paper is to study triple difference sequence spaces over $n$-normed space via the sequence of modulus functions. Some algebraic and topological properties of the newly constructed spaces are also established.

In this paper, we introduce the operator approach for orthogonality in linear spaces. In particular, we represent the concept of orthogonal vectors using an operator associated with them, in normed linear spaces.

We establish the existence of at least three distinct weak solutions for a perturbed nonlocal fourth-order Kirchhoff-type problem with Navier boundary conditions under appropriate hypotheses on nonlinear terms. Our main tools are based on variational methods and some critical points theorems. We give some examples to illustrate the obtained results.

In this paper, we first introduce the notion of an $(m,n)$-quasi-hyperideal in an ordered semihypergroup and, then, study some properties of $(m,n)$-quasi-hyperideals for any positive integers $m$ and $n$. Thereafter, we characterize the minimality of an $(m,n)$-quasi-hyperideal in terms of $(m,0)$-hyperideals and $(0,n)$-hyperideals respectively. The relation $\mathcal{Q}_m^n$ on an ordered semihypergroup is, then, introduced for any positive integers $m$ and $n$ and proved that the relation $\mathcal{Q}_m^n$ is contained in the relation $\mathcal{Q}=\mathcal{Q}_1^1$. We also show that, in an $(m,n)$-regular ordered semihypergroup, the relation $\mathcal{Q}_m^n$ coincides with the relation $\mathcal{Q}$. Finally, the notion of an $(m,n)$-quasi-hypersimple ordered semihypergroup is introduced and some properties of $(m,n)$-quasi-hypersimple ordered semihypergroups are studied. We further show that, on any $(m,n)$-quasi-hypersimple ordered semihypergroup, the relations $\mathcal{Q}_m^n$ and $\mathcal{Q}$ are equal and are universal relations.

Let $L$ be a $C$-lattice and $M$ be a lattice module over $L$. For a non-zero element $N\in M$, join of all second elements $X$ of $M$ with $X\leq N$ is called the second radical of $N$, and it is denoted by $\sqrt[s]{N}$. In this paper, we study some properties of second radical of elements of $M$ and obtain some related results.