Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

Based on a notion of relatively maximal (m)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions

Optical and interferometric studies of growth phenomena on carborundum crystals

The theory of the growth of a perfect crystal is outlined and a brief description is given of the development of this theory, taking into account the presence of imperfections, especially dislocations, in the crystal. The molecular 'growth spirals' and other features predicted by this theory put forward by Burton, Cabrera and Prank require improved experimental techniques for their study, which are described. The experimental study of the growth features divides itself into two parts: (1) Microscopic studies. (2) Interferometric studies. The different growth features observed on the faces of silicon-carbide (Si-C) crystals are illustrated and explained. The observed 'growth spirals' can be divided into three types: (1) Elementary spirals with step heights equal to the size of the X-ray unit cell. (2) Spirals originating from dislocations of multiple strength, the step heights being a multiple of the X-ray unit cell. (3) Interlaced spirals in which the step heights are a fraction of the unit cell. The microscopic studies illustrate the information about the shape of the spirals, the behaviour and interaction of growth fronts with one another, originating from different sources, the growth pattern for a number of screw dislocations emerging on the crystal face fault surfaces, and their statiscal properties such as density of dis-locations etc. From these studies the type of information obtainable about the conditions of growth is the size of the critical nucleus and the supersaturation. The interferometric techniques utilized for the measurement of step heights are discussed. A study of the measured step heights leads to an understanding of the interesting property of 'polytypism' as observed in silicon-carbide crystals which occur in different types as shown by X-ray diffraction data. The 'growth spirals' demonstrate the X-ray predictions and confirm them.<p

Fixed Points for Ciric-G-Contractions in Uniform Spaces Endowed with a Graph

In this paper, we generalize the notion of $\lambda$-generalized contractions introduced by \'Ciri\'c from metric to uniform spaces endowed with a graph and discuss on the existence and uniqueness of fixed points for this type of contractions using the basic entourages.Comment: 12 page

Valuing Quality in Educational Services: An Empirical Study

This study aims to evaluate the value parameters in education services and to develop a framework for enhancement of student’s satisfaction. Focusing on traditional service quality dimensions and new concerns, it seeks to investigate the changes in expectations due to changing trends in education service industry and level of performance achieved with the identification of gap areas.   This paper reviews emerging gaps in service performance in education sector with the help of primary study. Respondents are selected on simple random basis from various formats of management institutes in India. Research instrument was designed with available scales in service quality studies with some new additions reflecting changed scenario. Data analysis reflects the gaps and the important dimensions which needs urgent attention.   The paper suggests that educational planners should look into the emerging trends and allocate their resources in light of importance-performance analysis. The findings of this study can be used by the practitioners in identification and improvement of service gap areas to enhance student’s satisfaction. Keywords: Service quality, Customer Satisfaction, Service Gap, Service Performanc