Some remarks on bv(s)-metric spaces and fixed point results with an application

We compare the newly defined bv(s)-metric spaces with several other abstract spaces like metric spaces, b-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in bv(s)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of bv(s)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki–Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm–Volterra integral equations

On Proximal contractions via implicit relations and Best proximity points

In this paper, we employ two types of implicit relations to define some new kind of proximal contractions and study about their best proximity points. More precisely, we use two class of functions $\mathcal{A}$ and $\mathcal{A}'$ to explore proximal $\mathcal{A}$, $\mathcal{A}'$-contractions of first and second type and strong proximal $\mathcal{A}$, $\mathcal{A}'$-contractions. We investigate the existence of best proximity point results of the same. It is worth mentioning that the well-known results of Sadiq Basha [J. Approx. Theory, $2011$] on proximal contractions are the special cases of our obtained results. We authenticate our results by suitable examples.Comment: 16 page

On Maia type fixed point results via implicit relation

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called $\mathcal{A}$-contraction and $\mathcal{A}'$-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper

Increased toll-like receptor-2 expression on nonclassic CD16⁺monocytes from patients with inflammatory stage of eales' disease

Purpose.: To identify the distribution, differential Toll-like receptor (TLR) expression, and functional contribution of monocyte subpopulations in the inflammatory stage of Eales' disease (ED). Methods.: Peripheral blood mononuclear cells were isolated from nine patients during the inflammatory stage of ED and nine age- and sex-matched healthy controls. The expression of CD14, CD16, TLR-2, and TLR-4 on monocytes was measured by flow cytometry. The CD14+, CD16−, and CD16+ monocyte populations were sorted on the basis of magnetic-activated cell-sorting methodology, and levels of cytokines were measured by ELISA. Results.: In ED patients, the number of circulating monocytes was significantly expanded compared with that in controls (P = 0.01), with a marked increase in the nonclassic CD16+ subset, which showed an activated phenotype in patients that correlated with levels of serum proinflammatory cytokines and clinical progression. A higher expression of cell surface TLR-2 (P = 0.02), but not TLR-4, was found in monocytes of patients with ED. Furthermore, TLR-2 was expressed at higher levels on CD16+ monocytes than on CD16− monocytes in patients, whereas no significant variation was found in TLR-4 expression on different monocyte subsets. Peptidoglycan-induced TNF-α expression correlated with TLR-2 expression in monocytes isolated from controls (r = 0.85, P = 0.0061), but not in monocytes isolated from ED patients (r = 0.553, P = 0.1328). Conclusions.: These results indicate that in the pathogenesis of ED, TLR activation and increased numbers of nonclassic CD16+ monocytes are crucial regulators, along with the secretion of proinflammatory cytokines that perpetuate the inflammatory process in the retina

Role of Lipid, Protein-Derived Toxic Molecules, and Deficiency of Antioxidants behind the Pathogenesis of Diabetic Retinopathy (DR) in Type 2 Diabetes Mellitus

To determine the role of NADPH-oxidase mediated formation of different lipid, protein-derived molecules, and depletion of vitamin-C level in vitreous behind the endothelial dysfunction-induced vascular endothelial growth factor secretion and pathogenesis of diabetic retinopathy (DR) in type 2 diabetes mellitus (T2DM). Fourteen T2DM patients with mild non-proliferative diabetic retinopathy (MNPDR), 11 patients without diabetic retinopathy (DNR), 17 T2 DM subjects with high-risk proliferative diabetic retinopathy (HRPDR), and 5 healthy individuals without DM underwent vitreous analysis for estimation NADPH oxidase, lipid peroxide like malondialdehyde (MDA), 4-Hydroxy-noneal (HNE) and advanced lipoxidation end product (ALE) like Hexanoyl-lysine (HLY), protein carbonyl compound (PCC), Vitamin-C and concentration of vascular endothelial growth factor (VEGF) secretion following standard spectrophotometric methods and enzyme-linked immunosorbent assay (ELISA). Vitreous concentration of NADPH-oxidase, different protein and lipid-derived molecule, and VEGF were found to be significantly elevated among DNR and of DR subjects with different grades compared to HC subjects whereasthe vitamin-C level was found to be decreased among different DR subjects and DNR subjects in comparison to healthy individuals. Oxidative stress-mediated lipid and protein-derived biomolecules not only add important mediators in the pathogenesis of DR, but also accelerate the progression and severity of microangiopathy

Biochemical scenario behind initiation of diabetic retinopathy in type 2 diabetes mellitus

Purpose: Despite the disease having similar glycemic status and duration microangiopathy in some patients develop within few years whereas it doesn't appear as a health complication in some diabetics for a considerable period. This study is undertaken to assess the hyperglycemia-induced biochemical background behind the development of diabetic retinopathy (DR) in type 2 diabetes mellitus (DM). Methods: Following proper diagnosis, 100 patients of type 2 DM of 10–12 years duration having no DR, and 42 patients of type 2 DM of the same duration and glycemic status as the second group, with mild retinopathy were recruited in the study. Lactic acid, glutamate, malondialdehyde (MDA), nitrate, advanced glycation end-products (AGEs), peripheral blood mononuclear cell reactive oxygen species (ROS), vascular endothelial growth factor (VEGF), and its receptor 2 (VEGFR2) in these two groups were produced in an assay following standard methodology. Results: Biochemical markers of anaerobic glycolysis, lipid peroxidation, AGEs, glutamate concentration, oxidative stress, and expression of VEGF and its VEGFR2 with significantly elevated markings were found in them who developed earliest stage of DR rather than them who had not. Conclusion: Hyperglycemia-induced anomalous glucose metabolism, lipid peroxidation, advanced glycation, glutamate toxicity, and oxidative stress create a background where apoptosis of retinal capillary endothelial cells invite increased expression of VEGF and VEGFR2, these being the crucial factors behind the development of diabetic microangiopathy