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

Nanoparticles of Pb_1-xCd_xS within the composition of 0≤x≤1 were prepared from the reaction of aqueous solution of cadmium acetate, lead acetate, thiourea, and NaOH by chemical co-precipitation. The prepared samples were characterized by UV-Vis spectroscopy(in the range 300-1100nm) to study the optical properties, AFM and SEM to check the surface morphology(Roughness average and shape) and the particle size. XRD technique was used to determine the crystalline structure, XRD technique was used to determine the purity of the phase and the crystalline structure, The crystalline size average of the nanoparticles have been found to be 20.7, 15.48, 11.9, 11.8, and 13.65 nm for PbS, Pb_0.75Cd_0.25S,

Throughout Agriculture has mostly relied on the use of natural fertilizers throughout human history, which are compounds that increase the nitrogen levels in the soil. Modern agriculture was made possible by the introduction of synthetic fertilizers at the end of the 19th centuryproduction of agriculture. Their application enhanced crop yields and sparked an agricultural revolution unlike anything the world had ever seen.In the near future, synthetic fertilizers are anticipated to continue to have a significant impa ct on human life, both positively and negatively. They are frequently utilized for producing all t ypes of crops and are essential to plant growth. The significance of synthetic fertilizers is their ability to provide the soil w

In this investigation, metal matrix composites (MMC_s) were manufactured by using powder technology. Aluminum 6061 is reinforced with two different ceramics particles (SiC and B₄C) with different volume fractions as (3, 6, 9 and 12 wt. %). The most important applications of particulate reinforcement of aluminum matrix are: Pistons, Connecting rods etc. The specimens were prepared by using aluminum powder with 150 µm in particle size and SiC, B₄C powder with 200 µm in particle size. The chosen powders were mixed by using planetary mixing setup at 250 rpm for 4hr.with zinc stearate as an activator material in steel ball milling. After mixing process the powders were compacted by hydraulic

This work aims to investigate the tensile and compression strengths of heat- cured acrylic resin denture base material by adding styrene-butadiene (S- B) to polymethyl methacrylate (PMMA). The most well- known issue in prosthodontic practice is fracture of a denture base. All samples were a blend of (90%, 80%) PMMA and (10%, 20%) S- B powder melted in Oxolane (Tetra hydro furan). These samples were chopped down into specimens of dimensions 100x10x2.5mm to carry out the requirements of tensile tests. The compression strength test specimens were shaped into a cylinder with dimensions of 12.7mm in diameter and 20mm in length. The experimental results show a significant increase in both tensile and compression strengths when compared to cont