On the generalized vector F-implicit complementarity problems and vector F-implicit variational inequality problems

In this paper, we introduce and analyze some new classes of generalized vector-F implicit complementarity problems and the general mixed vector-F variational inequalities. Under suitable conditions, we prove the equivalences between these new problems. We establish several existence theorems for these classes of vector-F complementarity and general mixed vector-F variational inequalities using a new version of the Fan-KKM theorem in Hausdorff topological vector spaces, and without even using the classical assumptions in this context, like monotonicity or continuity. Results obtained in this paper represent significant improvement and refinement of the previously known results

New kinds of generalized variational-like inequality problems in topological vector spaces

AbstractIn this work, we consider a generalized nonlinear variational-like inequality problem, in topological vector spaces, and, by using the KKM technique, we prove an existence theorem. Our result extends a theorem of Ahmad and Irfan [R. Ahmad, S.S. Irfan, On the generalized nonlinear variational-like inequality problems, Appl. Math. Lett. 19 (2006) 294–297]

A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result

The relative frequency, clinical and laboratory findings of adult glomerulonephritidies in Tehran

Background: Renal diseases information is population-based and has great geographic variability. Due to the lack of national renal data registry system, there is no information on the prevalence rate, and clinical and laboratory features of various glomerulonephritidies (GNs) in Iran. Methods: In a retrospective cross sectional study, we analyzed 462 adult renal biopsies in Hashemi Nejad hospital, Tehran, Iran. We determined the prevalence rate and the frequency of different clinical and laboratory findings in patients with different GNs. We also compared our results with the reports from other countries. Results: There were 267(57.8) males and 195(42.2) females. The mean age (± SD) was 33.6 ± 15.7 (range, 13-75) years old. After exclusion of 55 biopsies with pathologies other than GNs and in the remaining 407 biopsies, membranous glomerulopathy (MGN) was the most common GN (23.6), followed by IgAN (13.5), membranoproliferative GN (11.5), systemic lupus nephritis (10.6), focal segmental glomerulosclerosis (10.3), and minimal change disease (9.8). These 6 GNs comprised the majority (79.4) of all GNs. Conclusion: MGN is the most common form of GN, followed by IgAN, MPGN, SLE-GN, FSGS and MCD in adult patients in our study. The multi-center studies with a larger sample size are needed for more comprehensive data in Iranian population

Best proximity point theorems for α-nonexpansive mappings in Banach spaces

In this paper, we discuss sufficient and necessary conditions for the existence of best proximity points for non-self-a-nonexpansive mappings in Banach spaces. We obtain convergence results under some assumptions, and we prove the existence of common best proximity points for a family of non-self-a-nonexpansive mappings