In this manuscript, we apply the simulation mappings to present and verify several original results of common and coincidence fixed point in complete S-metric spaces. Moreover, using S-metric to expand and generalized diverse results in the literature involving simulation mappings. On the other hand, we apply our major results to derive several common and coincidencefixed point theorems for right monotone simulation map in complete S-metric. As implementations, various related outcomes of fixed-point theory via specific simulation mappings are obtained in complete S-metric spaces. Additionally, illustrative examples and some applications to solve an integral equation are introduced to support our major results.

American scientific publishing group

The main objective of present paper, is to introduce and study other new weak forms of both slightly and almost slightly open mappings which are called slightly E-open (resp. slightly δ−ß−open) mappings, almost slightly E−open (resp. almost slightly δ−ß−open) mappings and almost somewhat E −open (resp. almost somewhat δ−ß−open) maps utilizing E−оpen and δ−ß −open sets respectively. Several of the fundamental properties related to these kinds of slight and almost slight open mappings have been investigated. In addition, the interrelationships between these ideas of mappings and other well-known related mappings have been discussed.

During the last few years, the study of generalized closed and open sets has fund considerable interest among general topologies, and they are most essential co During the last few years, the study of generalized closed and open sets has fund considerable interest among general topologies, and they are most essential co

The concept of generalized compactness is very useful and essential concept not only in general topology but also in the other advanced branches of pure and applied mathematics. As well one can observe the influence of topological spaces in computer sciences,digital topology, computational topology for geometric and molecular design particle physics, high energy physics, quantum physics and super-string theory. Therefore, new concepts of generalized compact spaces namely, ωδ-ß-compact and nearly ωδ-ß-compact space based on new generalized ω-open sets have been presented in topological spaces. In the process, various essential characterizations related to these kinds of generalized compact spaces have been investigated. Furthermore, the relationships among some kinds of generalized compact spaces have been discussed. As well, some illustrative examples to highlight the realized improvements are supplied.We expect that the discoveries in this article will aid scientists in developing the researches on general topology in order to elevate a general framework for their practical applications in all advanced branches of mathematics and other sciences.

Our article present and investigate another extension for the classical meaning of soft connectedness and soft Lindelöfness, namely almost soft E −compactness and almost soft E −Lindelofness via employing another idea of soft sets namely soft E −open. Various essential properties and some examples to explain the relationships among these spaces have been introduced. As well, the behavior of these spaces under soft E −irresolute mappings has been discussed. Additionally, several finding which connect between some generalized soft connectedness and Lindelöfness which are introduced in our article and some soft topological forms such as soft E −connected spaces and soft E−𝒯₂-spaces have been deduced.