Fibrewise topological spaces theory is a relatively new branch of mathematics, less than three decades old, arisen from algebraic topology. It is a highly useful tool and played a pivotal role in homotopy theory. Fibrewise topological spaces theory has a broad range of applications in many sorts of mathematical study such as Lie groups, differential geometry and dynamical systems theory. Moreover, one of the main objects, which is considered in fibrewise topological spaces theory is connectedness. In this regard, we of the present study introduce the concept of connected fibrewise topological spaces and study their main results.

The aim of this paper is to introduce and study some of the Fibrewise minimal regular,Fibrewise maximal regular, Fibrewise minimal completely regular, Fibrewise maximal completely regular, Fibrewise minimal normal, Fibrewise maximal normal, Fibrewise minimal functionally normal, and Fibrewise maximal functionally normal. This is done by providing some definitions of the concepts and examples related to them, as well as discussing some properties and mentioning some explanatory diagrams for those concepts.

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

Image quality plays a vital role in improving and assessing image compression performance. Image compression represents big image data to a new image with a smaller size suitable for storage and transmission. This paper aims to evaluate the implementation of the hybrid techniques-based tensor product mixed transform. Compression and quality metrics such as compression-ratio (CR), rate-distortion (RD), peak signal-to-noise ratio (PSNR), and Structural Content (SC) are utilized for evaluating the hybrid techniques. Then, a comparison between techniques is achieved according to these metrics to estimate the best technique. The main contribution is to improve the hybrid techniques. The proposed hybrid techniques are consisting of discrete wavel

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.