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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]

In this paper, we solve the existence and uniqueness of a solution for a fractional differential equation by introducing some new fixed point results for rational (αβ)-contractions in the framework of orthogonal F-metric spaces. We derive some well-known results in literature as consequences of our leading result. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define a Berinde type ( ρ , μ)- ϑ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to obtain common fixed point results in b-metric spaces for generalized rational contractions involving control functions of two variables. We provide an example to show the originality of our main result. As outcomes of our results, we derive certain fixed and common fixed point results for rational contractions presuming control functions of one variable and constants. As an application, we investigate the solution of an integral equation. [ABSTRACT FROM AUTHOR]

Metric fixed-point theory has become an essential tool in computer science, communication engineering and complex systems to validate the processes and algorithms by using functional equations and iterative procedures. The aim of this article is to obtain common fixed point results in a bicomplex valued metric space for rational contractions involving control functions of two variables. Our theorems generalize some famous results from literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the context of bicomplex valued metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a generalized (α, ΘF)-contraction in the context of an orthogonal F-complete metric space and obtain some new fixed point results for this newly introduced contraction. A nontrivial example is also provided to satisfy the validity of the established results. As consequences of our obtained results, we derive the leading results in [Fixed Point Theory Appl., 2015,185, 2015] and [Symmetry, 2020, 12,832]. As an application, we investigate the existence and uniqueness of the solution for a nonlinear fractional differential equation. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results on complex-valued extended b-metric spaces for rational contractions involving control functions of two variables. Our theorems generalize some famous results in the literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the class of complex-valued extended b-metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of F-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of F-metric space equipped with a directed graph G are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to establish some common fixed point results for generalized contractions including some precise control functions of two variables in the setting of controlled metric spaces. As consequences of our leading results, we derive common fixed point and fixed point results for contractions with control functions of one variable and constants. We also discuss controlled metric spaces endowed with a graph and obtain some common fixed point results in this newly introduced space. As an application of our leading result, we examine the solution of a Fredholm type integral equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a fractal of generalized Θ-Hutchinson Operator with the help of a finite family of Θ-contraction mappings, a class of mappings more general than contractions, defined on a complete metric space. Our results unify, generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The purpose of this article is to introduce locally α - ζ -multivalued contraction and rational Ćirić type α - ζ -multivalued contraction in the context of F -metric spaces and prove some endpoint results. We provide a nontrivial example to show the authenticity of our main result. Our results generalize some well-known results of literature. We also present some endpoint results in both graphic F -metric spaces and ordered F -metric spaces. As an application of our main result, we investigate the solution of an integral equation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to utilize complex valued extended b -metric space and obtain common α -fuzzy fixed point theorems under Kannan type contractions. As application, we derive common α -fixed point results for multivalued mappings in the context of complex valued extended b -metric space. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to solve the Fredholm integral inclusion for L-fuzzy mapping in the setting of complete b-metric spaces. To attain this target, we obtain some common L-fuzzy fixed point results for L-fuzzy mappings under F-contraction and derive the main results of Ahmad et al. [Fuzzy fixed points of fuzzy mappings via F-contractions and an applications, J. Intelligent Fuzzy Syst. 38 (2019), pp. 1–7] and Cosentino et al. [Solvability of integrodifferential problems via fixed point theory in b-metric spaces, Fixed Point Theor. Appl. 70 (2015), pp. 1–15]. To justify the notions and outcomes, we also demonstrate an appropriate example. [ABSTRACT FROM AUTHOR]