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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]

The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and (α , η) -Reich type interpolative contraction in the framework of orthogonal F -metric space and prove some fixed point results. Our primary result serves as a cornerstone, from which established findings in the literature emerge as natural consequences. To enhance the clarity of our novel contributions, we furnish a significant example that not only strengthens the innovative findings but also facilitates a deeper understanding of the established theory. The concluding section of our work is dedicated to the application of these results in establishing the existence and uniqueness of a solution for a fractional differential equation of anomalous diffusion. [ABSTRACT FROM AUTHOR]

The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions and a pair of self-mappings. In this way, we generalize some well-known results of literature. Some non-trivial examples are also flourished to demonstrate the innovation of our principal result. [ABSTRACT FROM AUTHOR]

Several nucleotide analogues have been approved for use in treating hepatitis B virus (HBV) infection. Long-term exposure to therapy leads to the emergence of mutations within the HBV DNA polymerase gene, resulting in drug resistance, a major factor contributing to therapy failure. Chronic HBV patients from the Khyber Pakhtunkhwa province, Pakistan, who had completed 6 months of therapy participated in this study. Samples were collected from 60 patients. In this study, the entire reverse transcriptase domain of the HBV polymerase gene was amplified using nested polymerase chain reaction and sequenced. Drug-resistant mutations were detected in nine (22.5%) patients. All of these patients had lamivudine-resistant mutations (rtM204V + L180M), while seven individuals (17.5%) had both lamivudine- plus entecavir-resistant mutations (L180M + M204V + S202G). N236T, a mutation that gives rise to tenofovir and adefovir resistance, was observed in two (5%) patients. T184A, a partial drug-resistant mutation to entecavir, was found in five (12.5%) patients. Furthermore, other genotypic variants (100%) and vaccine escape mutations (5%) were additionally observed. Moreover, pN459Y (35%), pN131D (20%), pL231S (20%), pP130Q (17.5%), pS189Q (12.5%), pP161S (5%), pH160P (2.5%), pT322S (2.5%), and pA223S (2.5%) mutations in the polymerase gene, as well as sA166V (17.5%), sQ181K (12.5%), sV184R (7.5%), sA17E (5%), sP153S/K (5%), sW156C (5%), sC76Y (2.5%), and S132F (2.5%) mutations in the small surface gene, were identified for the first time in this study. Phylogenetic analysis showed that genotype D was predominant amongst the HBV carriers. Subtype D1 was found in most patients, while two patients were subtype D9. These novel findings may contribute to the body of knowledge and have clinical significance for treating and curing HBV infections in Pakistan. [ABSTRACT FROM AUTHOR]

The aim of the present research article is to solve the system of linear equations using common fixed point theorems in the context of bicomplex valued metric spaces. To obtain our main objective, we introduce generalized contractive conditions in bicomplex valued metric spaces and establish common fixed point theorems for self mappings. We also give a significant example to demonstrate the legitimacy of the given theorems. [ABSTRACT FROM AUTHOR]

Urinary tract infections (UTIs) are healthcare problems that commonly involve bacterial and, in some rare instances, fungal or viral infections. The irrational prescription and use of antibiotics in UTI treatment have led to an increase in antibiotic resistance. Urine samples (145) were collected from male and female patients from Lower Dir, Khyber Pakhtunkhwa (KP), Pakistan. Biochemical analyses were carried out to identify uropathogens. Molecular analysis for the identification of 16S ribosomal RNA in samples was performed via Sanger sequencing. Evolutionary linkage was determined using Molecular Evolutionary Genetics Analysis-7 (MEGA-7). The study observed significant growth in 52% of the samples (83/145). Gram-negative bacteria were identified in 85.5% of samples, while Gram-positive bacteria were reported in 14.5%. The UTI prevalence was 67.5% in females and 32.5% in males. The most prevalent uropathogenic bacteria were Klebsiella pneumoniae (39.7%, 33/83), followed by Escherichia coli (27.7%, 23/83), Pseudomonas aeruginosa (10.8%, 9/83), Staphylococcus aureus (9.6%, 8/83), Proteus mirabilis (7.2%, 6/83) and Staphylococcus saprophyticus (4.8%, 4/83). Phylogenetic analysis was performed using the neighbor-joining method, further confirming the relation of the isolates in our study with previously reported uropathogenic isolates. Antibiotic susceptibility tests identified K. pneumonia as being sensitive to imipenem (100%) and fosfomycin (78.7%) and resistant to cefuroxime (100%) and ciprofloxacin (94%). Similarly, E. coli showed high susceptibility to imipenem (100%), fosfomycin (78.2%) and nitrofurantoin (78.2%), and resistance to ciprofloxacin (100%) and cefuroxime (100%). Imipenem was identified as the most effective antibiotic, while cefuroxime and ciprofloxacin were the least. The phylogenetic tree analysis indicated that K. pneumoniae, E. coli, P. aeruginosa, S. aureus and P. mirabilis clustered with each other and the reference sequences, indicating high similarity (based on 16S rRNA sequencing). It can be concluded that genetically varied uropathogenic organisms are commonly present within the KP population. Our findings demonstrate the need to optimize antibiotic use in treating UTIs and the prevention of antibiotic resistance in the KP population. [ABSTRACT FROM AUTHOR]

MicroRNAs miR-29a and miR-192 are involved in inflammatory and fibrotic processes of chronic liver disease, and circulating miR-29a is suggested to diagnose fibrosis progression due to hepatitis C virus (HCV) infection. This study aimed to evaluate the expression profile of circulating miR-192 and 29a in a patient cohort with a high frequency of HCV genotype-3. A total of 222 HCV blood samples were collected and serum were separated. Patients were classified into mild, moderate, and severe liver injury based on their Child–Turcotte–Pugh CTP score. RNA was isolated from the serum and used for quantitative real-time PCR. The HCV genotype-3 (62%) was the predominant HCV genotype. In HCV patients, the serum miR-192 and miR-29a levels were significantly upregulated in comparison to healthy controls (p = 0.0017 and p = 0.0001, respectively). The progression rate of miR-192 and 29a in the patient group with mild was highly upregulated compared to patients with moderate and severe hepatitis infection. The ROC curve of miR-192 and miR-29a of moderate liver disease had a significant diagnostic performance compared to the other HCV-infected groups. The increase in miR-29a and miR-192 serum levels was even slightly higher in patients with HCV genotype-3 than in non-genotype-3 patients. In conclusion, serum miR-192 and miR-29a levels significantly increased during the progression of chronic HCV infection. The marked upregulation in patients with HCV genotype-3 suggests them as potential biomarkers for hepatic disease, independently of the HCV genotype. [ABSTRACT FROM AUTHOR]

Zinc oxide nanoparticles (ZnO NPs) are the second most prevalent metal oxide, owing to their characteristics of low cost, safe, and easily prepared. ZnO NPs have been found to exhibit unique properties which show their potential to be used in various therapies. Numerous techniques have been devised for the manufacture of zinc oxide because it is one of the nanomaterials that has received major research interest. Mushroom sources are proven to be efficient, ecologically friendly, inexpensive, and safe for humankind. In the current study, an aqueous fraction of methanolic extract of Lentinula edodes (L. edoes) was used to synthesize ZnO NPs. The biosynthesis of ZnO NPs was achieved by using the reducing and capping capability of an L. edodes aqueous fraction. Bioactive compounds from mushroom, such as flavonoids and polyphenolic compounds, are used in the green synthesis process to biologically reduce metal ions or metal oxides to metal NPs. Biogenically synthesized ZnO NPs were further characterized by using UV–Vis, FTIR, HPLC, XRD, SEM, EDX, zeta sizer and zeta potential analyses. The FTIR showed the functional group at the spectra in the range 3550–3200 cm−1 indicated the presence of the hydroxyl (OH) group, while bands in the range 1720–1706 cm−1 indicated C=O carboxylic stretches bonds. Furthermore, the XRD pattern of ZnO NPs created in the current study was found to be nanocrystals which are hexagonal. The SEM analysis of ZnO NPs showed spherical shapes and size distributions in the range 90–148 nm. Biologically synthesized ZnO NPs have substantial biological activities including antioxidant, antimicrobial, antipyretic, antidiabetic and anti-inflammatory potential. Biological activities showed significant antioxidant (65.7 ± 1.09), antidiabetic (85.18 ± 0.48), and anti-inflammatory potential (86.45 ± 0.60) at 300 µg inhibition in paw inflammation of (1.1 ± 0.06) and yeast-induced pyrexia (97.4 ± 0.51) at 10 mg in a dose-dependent manner. The outcomes of this research indicated that ZnO NPs significantly reduced inflammation and have the ability to scavenge free radicals and prevent protein denaturation, while also indicating their possible use in food and nutraceutical applications to treat various ailments. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the authenticity of established outcomes. As an application, we investigate the solution of an Urysohn integral equation by applying our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of Perov–Ćirić–Prešić-type Θ -contractions and to obtain some generalized fixed point theorems in the setting of vector-valued metric spaces. We derive some fixed point results as consequences of our main results. A nontrivial example is also provided to support the validity of our established results. As an application, we investigate the solution of a semilinear operator system in Banach space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations. [ABSTRACT FROM AUTHOR]

F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α -fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α -fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature. [ABSTRACT FROM AUTHOR]

This paper is designed to display some results which generalize the recent results that cannot be established from the corresponding results in other spaces and do not satisfy the remarks of Jleli et al. (Fixed Point Theor Appl. 210, 2012) and Samet et al. (Int. J. Anal. Article ID 917158, 2013). We obtain unique fixed-point for mapping satisfying β - ψ ˇ contraction only on a closed G d ball in complete dislocated G d -metric space. An example is also discussed to shed light on the main result. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2). [ABSTRACT FROM AUTHOR]

The aim of this article is to establish some fixed point results for fuzzy mappings and derive some corresponding multivalued mappings results of literature. For this purpose, we define some new and generalized contractions in the setting of b-metric spaces. As applications, we find solutions of integral inclusions by our obtained results. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define generalized ( α β - ψ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / (ι) = − ρ 1 (ι) ϑ (ι) + ρ 2 (ι) L (ϑ (ι − ς (ι))) + ρ 3 (ι) ϑ / (ι − ς (ι)) , where ρ 1 (ι) , ρ 2 (ι) are continuous, ρ 3 (ι) is continuously differentiable and ς (ι) > 0 , for all ι ∈ R and is twice continuously differentiable. [ABSTRACT FROM AUTHOR]

Best proximity point theorem furnishes sufficient conditions for the existence and computation of an approximate solution ω that is optimal in the sense that the error σ (ω , J ω) assumes the global minimum value σ (θ , ϑ) . The aim of this paper is to define the notion of Suzuki α - Θ -proximal multivalued contraction and prove the existence of best proximity points ω satisfying σ (ω , J ω) = σ (θ , ϑ) , where J is assumed to be continuous or the space M is regular. We derive some best proximity results on a metric space with graphs and ordered metric spaces as consequences. We also provide a non trivial example to support our main results. As applications of our main results, we discuss some variational inequality problems and dynamical programming problems. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ (t) ∈ f (t) + ∫ 0 1 K (t , s , φ (s)) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v (R) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized ( α , φ ) rational contraction, as well as cyclic contractions in the context of F -metric spaces. We also supply an example to support the new theorem. [ABSTRACT FROM AUTHOR]

Using the concept of binary relation R , we initiate a notion of Θ R -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]