On Existence of Coincidence and Common Fixed Points for Weakly Compatible Self Maps in Normed Boolean Vector Space

In this paper we discuss existence of coincidence and common fixed points for two pairs of weakly compatible self maps in Normed Boolean Vector Space. Our results extend and improve the results of Mishra et al. [8] and others existing in the literature. Some illustrative examples to highlight the validity of obtained results are also furnished. Keywords: Weakly compatible maps, coincidence point, common fixed point, Normed Boolean vector space, Boolean metric

Coincidence and common fixed point theorems for faintly compatible maps

The paper is aimed to generalize and improve the results of Bisht and Shahzad [Faintly compatible mappings and common fixed points, fixed point theory and applications, 2013, 2013:156]. The significance of this paper lies in the fact that coincidence and common fixed point theorems under Ciri´c type contractive condition ´ via faint compatibility and conditional reciprocal continuity is established without using continuity of even single map and containment requirement of the range space of involved maps. Illustrative examples are furnished to highlight the realized improvement of our results.Publisher's Versio

Fixed points and its applications in C*- algebra valued partial metric space

We familiarise with the concepts of contractiveness and expansiveness in a C*- algebra valued partial metric space and create an environment for the existence of fixed point in it. We solve an integral equation and an operator type equation as an application of main result. Further we give some examples to elaborate C*- algebra valued partial metric space and show that there exist situations when a partial metric result can be applied, while the standard metric one cannot.Publisher's Versio

On coincidence and common fixed point of six maps satisfying f-contractions

Coincidence and common fixed point of six self maps satisfying F-contractions are established via common limit in the range property without exploiting the notion of continuity or containment of range space of involved maps or completeness of space/subspace. Our results generalize, extend and improve the analogous recent results in literature.Publisher's Versio

On fixed points, their geometry and application to satellite web coupling problem in S−metric spaces

We introduce an M−class function in an S−metric space which is a viable, productive, and powerful technique for finding the existence of a fixed point and fixed circle. Our conclusions unify, improve, extend, and generalize numerous results to a widespread class of discontinuous maps. Next, we introduce notions of a fixed ellipse (elliptic disc) in an S−metric space to investigate the geometry of the collection of fixed points and prove fixed ellipse (elliptic disc) theorems. In the sequel, we validate these conclusions with illustrative examples. We explore some conditions which eliminate the possibility of the identity map in the existence of an ellipse (elliptic disc). Some remarks, propositions, and examples to exhibit the feasibility of the results are presented. The paper is concluded with a discussion of activation functions that are discontinuous in nature and, consequently, utilized in a neural network for increasing the storage capacity. Towards the end, we solve the satellite web coupling problem and propose two open problems

Data pre-processing for the preterm prediction study MFMU dataset

Preterm birth is a major public health problem with profound implications on society. There would be extreme value in being able to identify women at risk of preterm birth during the course of their pregnancy. Previous research has largely focused on individual risk factors correlated with preterm birth (e.g. prior preterm birth, race, and infection) and less on combining these factors in a way to understand the complex etiologies of preterm birth. We attempt to address this gap by conducting a deeper analysis of the preterm prediction study data collected by the NICHD Maternal Fetal Medicine Units (MFMU) Network, a high-quality data for over 3,000 singleton pregnancies having detailed study visits and biospecimen collection at 24, 26, 28 and 30 weeks gestation. Reports from this dataset used relatively straightforward biostatitistical methodologies such as relative risk assessments to measure associations between risk factors and PTB (Maternal Fetal Medicine Units Net- work. Biostatistical Coordinating Center NICHD Networks, 1995). These methods include descriptive statistics, Pearson correlation, Fisher’s exact tests and linear/logistic regression where risk factors are studied independent of each other. In order to perform detailed experiments on this data using non-linear Support Vector Machines and other machine learning (ML) methodologies, it is necessary to complete several pre-processing steps that we describe in this report

Fractals as Julia and Mandelbrot Sets of Complex Cosine Functions via Fixed Point Iterations

In this manuscript, we explore stunning fractals as Julia and Mandelbrot sets of complexvalued cosine functions by establishing the escape radii via a four-step iteration scheme extended with s-convexity. We furnish some illustrations to determine the alteration in generated graphical images and study the consequences of underlying parameters on the variation of dynamics, colour, time of generation, and shape of generated fractals. The black points in the obtained fractals are the “non-chaotic” points and the dynamical behaviour in the black area is easily predictable. The coloured points are the points that “escape”, that is, they tend to infinity under one of iterative methods based on a four-step fixed-point iteration scheme extended with s-convexity. The different colours tell us how quickly a point escapes. The order of escaping of coloured points is red, orange, yellow, green, blue, and violet, that is, the red point is the fastest to escape while the violet point is the slowest to escape. Mostly, these generated fractals have symmetry. The Julia set, where we find all of the chaotic behaviour for the dynamical system, marks the boundary between these two categories of behaviour points. The Mandelbrot set, which was originally observed in 1980 by Benoit Mandelbrot and is particularly important in dynamics, is the collection of all feasible Julia sets. It perfectly sums up the Julia sets

A COMPARATIVE ANALYSIS OF PRIMARY & SECONDARY SCHOOL TEACHERS IN REFERENCE TO THEIR SELF CONFIDENCE

<p>In the present study, an attempt has been made to compare the self confidence of primary and secondary school teachers of Bareilly District on the basis of 10 areas :-I- Physical Confidence, II - Technological Confidence, III - Social Confidence, IV - Psychological Confidence, V - Judgment Confidence, VI - Readiness Confidence, VII - Environment Confidence, VIII - Stage confidence, IX - Status confidence, X - Peer Independence Confidence. This study has been conducted on a sample of 114 primary and secondary school teachers selected randomly from schools affiliated to C.B.S.E. & U.P. Board. The main finding of the study exhibited significant difference between male and female, primary and secondary school teachers of C.B.S.E & U.P. Board. Male teachers were found to posses more physical confident as compared to that of female teachers. Further, significant difference in physical confidence was also found between male and female teachers of primary and secondary schools. No significant difference was found in other dimensions such as:-Technological Confidence, Social Confidence, Psychological Confidence, Judgment Confidence, Readiness Confidence, Environment Confidence, Stage Confidence, Status Confidence and Peer Independence Confidence.</p> <p> </p&gt

A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation

In this paper, we introduce the notion of subsequential continuity for a hybrid pair of maps and combine this concept with compatibility, to establish a coincidence and common fixed point theorem for a hybrid quadruple of maps. Our main result also demonstrates that several fixed point theorems can be unified using implicit relations. We also give two examples in support our results