In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach contraction principle to include metric space with modular spaces has been included in some recent research, the aim of study proves some pro

Research summary

Muslim scholars have established fundamental rules for deriving rulings to be a methodology for every mujtahid who wants to extract rulings from his reliable sources, and one of the most prominent fundamental rules on which many rulings are built is the permissible and the many rulings related to it.

Leaving what is permissible on its own terms sometimes causes embarrassment and distress in some cases, so we need something that restricts it. In our Islamic law, many legal rulings are embodied in which the restriction of what is permissible is in the public interest, or to relieve embarrassment in public.

Because of the importance of this fundamentalist rule, and the difference in some

This research investigates the methods of producing Investigative Arabic Television Programs that are able to prove its existence during a short period of time as a form of Television programs on Arab satellite channels growing in number and varied in content. The research aims to present qualitative and quantitative descriptions of the methods used in tackling the topics discussed in the program, and knowing whether they satisfy the conditions and scientific foundations for the research, investigation, analysis, and interpretation. The researcher uses the survey method and uses the tool of content analysis including a set of methodological steps that seek to discover the implied meaning of the research sample represented by the program

In this research, production of ethanol from waste potatoes fermentation was studied using Saccharmyses cerevisiae. Potato Flour was prepared from potato tubers after cooking and drying at 85°C. Homogenous slurry of potato flour was prepared in water at solid liquid ratio 1:10. Liquefaction of potato flour slurry with α-amylase at 80°C for 40 min followed by saccharification with glucoamylase at 65°C for 2 hr .Fermentation of hydrolysate with Saccharomyces cerevisiae at 35°C for two days resulted in production of 33 g/l ethanol.

      The parameters studied were; temperature, time of fermentation and pH. It was found that Saccharification process is affected by enzyme Amylo 300 conc