The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ R (where R = 1 + xZ x ) can be written as f = gn for g ∈ R, n 2. Let Pn := {gn | g ∈R} and let μn := n∏p |n p. We show among other things that (i) for f ∈R, f ...

Abstract Let ${\textbf{G}}$ be a connected reductive algebraic group defined over finite field $\mathbb{F}_q$ of $q$ elements and $\textbf{B}$ Borel subgroup $\mathbb{F}_q$. $\mathbb{k}$ we assume that $\mathbb{k}=\bar{\mathbb{F}}_q $ when $\textrm{char}\ \mathbb{k}=\textrm{char} \ \mathbb{F}_q$. We show the abstract-induced module $\mathbb{M}(\theta )=\mathbb{k}{\textbf{G}}\otimes _{\mathbb{k}...

A very wide angle lens with a field of view 360°x180° - fisheye has been designed to be used in space environment. As case study, the is assumed mounted on spinning probe passing through comet’s tail. The lens, rotating comet coma, may map entire sky as viewed from interior tail, providing unprecedented data spatial distribution plasma and dust. Considering foreseen applications for radiation h...

In this paper, we study the existence of fixed points for mappings defined on complete metric space (X, d) satisfying a general contractive inequality depended on another function. This conditions is analogous of Banach conditions and general contraction condition of integral type.

The aim of this manuscript is to introduce a novel concept called Jaggi-type hybrid (ϕ -F)-contraction and establish some fixed point results for class contractions in the framework G-metric space. validity main result shown by suitable example realized improvements with respect corresponding literature are highlighted. By using constructed example, it observed that established herein cannot be...

‎‎a natural generalization of two dimensional cyclic code ($t{tdc}$) is two dimensional skew cyclic code‎. ‎it is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $r_n:=f[x,y;rho,theta]/_l$‎. ‎in this paper we characterize the left ideals of the ring $r_n$ with two methods and find the generator matrix for two dimensional s...