Fixed points and best approximation in Menger convex metric spaces

summary:We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space

Common random fixed points of compatible random operators

We construct a random iteration scheme and study necessary conditions for its convergence to a common random fixed point of two pairs of compatible random operators satisfying Meir-Keeler type conditions in Polish spaces. Some random fixed point theorems for weakly compatible random operators under generalized contractive conditions in the framework of symmetric spaces are also proved

Maternal and foetal outcome of acute kidney injury in pregnancy single centre experience from North India

Background: The diagnosis and treatment of acute kidney injury in pregnancy is a challenge to the physician as various pathophysiological changes take place during pregnancy, variability of symptoms and occasionally overlapping laboratory and clinical features. The occurrences of feto-maternal mortality associated with it decreased in developing nations due to increased prenatal and postnatal care and improved medical facilities. This study was undertaken to provide insight into feto-maternal outcome in patients presenting with acute kidney injury (AKI) during pregnancy. Methods: This was an open label prospective hospital-based cohort study comprising patients admitted in obstetrics and nephrology wards, presenting with AKI and no known chronic illnesses prior to pregnancy. Following criteria were used to diagnose AKI during pregnancy: (a) Elevation of S. creatinine ≥ 1 mg/dl; (b) Oligo-anuria for ≥ 12 hours and (c) Need for RRT. 50 such cases were enrolled in the study. Results: Out of all patients enrolled, majority (60%) had improved renal function, 16% expired, and 24% had no recovery in renal function. Out of all patients taken for haemodialysis, 20% of patients had improved renal function, 20% expired and 60% had no recovery in renal function. Mean S. creatinine on 3 months follow-up in conservative group found-1.67±1.31 mg/dl. 60% pregnancies resulted in the birth of a live baby and rest resulted in foetal loss. Conclusions: In our study, it was found that acute kidney injury in pregnancy results in significant feto-maternal mortality and morbidity. Those patients, who had significant renal derangement and concomitant complications, had poorer outcome

Periodic fixed points of random operators

Sufficient conditions for existence of random fixed point of a nonexpan- sive rotative random operator are obtained and existence of random periodic points of a random operator is proved. We also derive random periodic point theorem for ǫ- expansive random operator

Fixed point results for set-contractions on metric spaces with a directed graph

In this paper, we establish the existence of fixed points for set-valued mappings satisfying certain graph contractions with set-valued domain endowed with a graph. These results unify, generalize, and complement various known comparable results in the literature.King Fahd University of Petroleum and Minerals project IN 121023.http://link.springer.com/journal/11784hb201

Convergence of iterative algorithms to common random fixed points of random operators

We prove the existence of a common random fixed point of two asymptotically nonexpansive random operators through strong and weak convergences of an iterative process. The necessary and sufficient condition for the convergence of sequence of measurable functions to a random fixed point of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces is also established

Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition

We prove the existence of coincidence point and common fixed point for mappings satisfying generalized weak contractive condition. As an application, related results on invariant approximation are derived. Our results generalize various known results in the literature

Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition

We prove the existence of coincidence point and common fixed point for mappings satisfying generalized weak contractive condition. As an application, related results on invariant approximation are derived. Our results generalize various known results in the literature.</p

Invariant approximation for fuzzy nonexpansive mappings

summary:We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all {$t$-best} approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric space is proved. Our results extend, generalize and unify various known results in the existing literature