In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

Purpose: To compare the therapeutic efficacy and safety of dorzolamide/timolol fixed-combination in newly diagnosed primary open angle glaucoma patients. Methods: In this prospective, interventional case series, newly diagnosed primary open angle glaucoma (POAG) patients that had not been treated for glaucoma were included. Patients were started on Cosopt twice a day (BID) for 1 month and then switched to three times a day (TDS) for additional 1 month. Patients underwent comprehensive ophthalmic examination, diurnal intraocular pressure (IOP), blood pressure (BP) and 24-hours heart rate (HR) measurements at baseline, month 1( BID), and month 2( TDS). IOP, systolic and diastolic pressures were measured at 8:00 AM,12:00 AM, 4:00 PM, 8:00 PM and 12:00 PM. Throughout the study, all adverse events were recorded and monitored by the investigators. Results: In 31 POAG patients that completed the study ,mean baseline IOP was 23.1±3.15 mmHg . IOP was decreased significantly 16.5 ± 2.21 at 1 month (P < 0.0001) and 13.9 ± 2.23 mmHg at 1 and 2 month follow up. (P < 0.0001) IOP was significantly lower in month 2 compared to month 1 (P = 0.0004). While Cosopt BID significantly reduced the mean 24-hour systolic BP and mean 24-hour HR from baseline (P < 0.0001), the mean 24-hour systolic BP and HR remained unchanged 2ith Cosopt TDS compared to BID (P = 0.62). Conclusions: Cosopt TDS has a superior IOP-lowering effect than Cosopt BID in POAG patients with comparable safety profile.

The purpose of this article is to characterize the Caristi type mapping by the absolute derivative. The equivalences of the Caristi mapping with contraction mapping is discussed too. In addition, it was shown that the contraction mapping can be characterized by its absolute derivative.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

With the increasing of copper consumption, the in-use stock of copper tends to increase. This paper used the “average use life method” to quantify the amount of copper in-use stock, and calculated the average age of in-use stock. It was indicated that the total in-use stock had an overall smooth trends, and reached its peak in 2007 was about 68.9 Mt (million tons), in addition, in-use stock per capita reached its peak ,234 kg/capita in 2001. The results demonstrated that during the period 1992-2002, the average age of copper in-use stock was continually decreased, but gradually increased since the year 2003. The fixed assets depreciation method used in this paper is applied to analyze depreciated copper in-use stock, and to analyze the relationship with economic indicator (GDP). It is demonstrated that it was inconsistent with the theory of Environmental Kuznets Curve (EKC) before 2000, this might be the demand for copper in the service sector is greater than the reduced strength of alternatives. Finally, scenario analysis of future copper in-use stock and depreciated copper in-use stock per capita in the U.S. were presented. The corresponding average age of the in-use stock will have a slight rise in the next decade.

Traffic congestion is one of the foremost problems confronted by the urban and suburban tenants of today. Traffic congestion increases vehicle emissions and degrades air quality. Urban planners and policy makers have consequently been always investigating choices to alleviate traffic congestion and to enhance air quality. Teleworking is one option that has received significant consideration and has been studied in the recent past. The aim of the study is to explore the relationship between teleworking, air quality and traffic in Switzerland. The analysis relies on panel individual and household level data over the period 2002-2013. We examine five main air pollutants; the sulphur dioxide (SO₂), the ground-level ozone (O₃) the nitrogen dioxide (NO₂), the carbon monoxide (CO) and the particulate matter less than 10 microns (PM₁₀). Based on the fixed effects estimates, teleworking reduces traffic volume by 1.9 per cent. Furthermore, the reduction observed on air pollution is higher for NO₂, CO and PM₁₀ ranging between 3.3-3.7 per cent, followed by O₃ at 2.3 per cent and SO₂ at 2.1 per cent. According to instrumental variable (IV) approach and the two stage least squares (2SLS) method, the effect is higher ranging between 2.6-4.1 per cent. The respective reduction on traffic becomes 2.7 per cent. Overall, the main concluding remark of the study is that teleworking can be a promising tool for urban planning and development, focusing at the traffic volume reduction, and the air quality improvement. Additional policy implications of teleworking and its beneficial effects for the society are further discussed.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

This paper uses panel data to find the determinants of tracking errors in exchange traded funds (ETFs) in the Hong Kong stock market. A comparison of tracking errors between physical and synthetic ETFs also indicates that the synthetic ETFs have higher tracking errors. The magnitude of tracking errors is found to be negatively related to size but positively related to dividend yield, trading volumes of funds, and market risk. However, this study also finds that expense ratio has a negative impact on tracking error, which is not consistent with previous studies, and which this paper addresses.