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This paper introduces the concept of proximal (α , F) -contractions in F -metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond. [ABSTRACT FROM AUTHOR]

In this publication, our objective was to introduce and establish the concepts of KGm-contraction and generalized (a, KGm)-contraction in complete Gm-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis. [ABSTRACT FROM AUTHOR]

The discovery of bioactive compounds from fungal natural sources holds immense potential for the development of novel therapeutics. The present study investigates the extracts of soil-borne Penicillium notatum and rhizosphere-inhabiting Aspergillus flavus for their antibacterial, antifungal, and cytotoxic potential. Additionally, two compounds were purified using chromatographic and spectroscopic techniques. The results demonstrated that the ethyl acetate fraction of A. flavus exhibited prominent cytotoxic activity against Artemia salina, whereas the ethyl acetate fraction of P. notatum displayed promising antibacterial potential. At dose concentrations of 10, 100, and 1000 µg mL−1, the ethyl acetate fraction of A. flavus showed mortality percentages of 7.6%, 66.4%, and 90%, respectively. The ethyl acetate fraction of P. notatum extract exhibited significant antibacterial activity, forming inhibition zones measuring 41, 38, 34, 34, and 30 mm against B. subtilis, S. flexneri, E. coli, K. pneumoniae, and S. aureus, respectively, at 1000 µg mL−1. At this concentration, inhibition zones of 28, 27, and 15 mm were recorded for P. vulgaris, S. typhi, and X. oryzae. Using bioassay-guided approach, one compound each was purified from the fungal extracts. The initial purification involved mass spectroscopic analysis, followed by structural elucidation using 500 MHz nuclear magnetic resonance (NMR) spectroscopy. Compound 1, derived from A. flavus, was identified as ethyl 2-hydroxy-5,6-dimethyl-4-oxocyclohex-2-ene-1-carboxylate, with a mass of 212, whereas compound 2, isolated from P. notatum, was identified as 3-amino-2-(cyclopenta-2,4-dien-1-ylamino)-8-methoxy-4H-chromen-4-one, with an exact mass of 270. Based on bioassay results, compound 1 was subjected to brine shrimp lethality assay and compound 2 was tested for its antibacterial potential. Compound 1 exhibited 30% lethality against brine shrimp larvae at a concentration of 100 µg mL−1, whereas at 1000 µg mL−1 the mortality increased to 70%. Compound 2 displayed notable antibacterial potential, forming inhibition zones of 30, 24, 19, and 12 mm against S. aureus, E. coli, B. subtilis, and S. flexneri, respectively. In comparison, the standard antibiotic tetracycline produced inhibition zones of 18, 18, 15, and 10 mm against the respective bacterial strains at the same concentration. [ABSTRACT FROM AUTHOR]

The purpose of this research article is to point out some fallacies in the statements of the main results of Rao et al. [Bull. Maths. Stat. Res] and Berrah et al. [AIMS Mathematics, 4(3)(2023), 1019{1033] and give a genuine contractive condition in the framework of complex valued b-metric spaces. We also introduce interpolative rational contractions in complex valued b-metric spaces and prove some fixed point results for such contractions. A non-trivial example is also provided to demonstrate the validity of obtained theorems. As an application, we investigate the existence of solutions for integral equations. [ABSTRACT FROM AUTHOR]