In this paper, we introduce the notion of generalized P D -operator pair with order n for single valued mappings and obtain some common fixed point theorems for generalized PD-operators on a set X equipped with the function F : X × X → ∆ without using the triangle inequality besides relaxing symmetric condition. Our results extend the results of Pathak and Rai [Common fixed points for PD -operator pairs under relaxed conditions with applications, Journal of Computational and Applied Mathematics, 239(1) (2013), 103– 113], Hussain et al.[Common fixed points for JH -operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal., 74 (2011), 2133-2140], Sintunavarat and Poom [Common fixed point theorems for generalized JH -operator classes and invariant approximations, Journal of ineqalities and Applications, 67 (2011)] and several others.

Chapter 8 Researching Bilingual and Multilingual Education Multilingually A Linguistic Ethnographic Approach Angela Creese, Angela CreeseSearch for more papers by this authorAdrian Blackledge, Adrian BlackledgeSearch for more papers by this authorArvind Bhatt, Arvind BhattSearch for more papers by this authorCarla Jonsson, Carla JonssonSearch for more papers by this authorKasper Juffermans, Kasper JuffermansSearch for more papers by this authorJinling Li, Jinling LiSearch for more papers by this authorPeter Martin, Peter MartinSearch for more papers by this authorAnu Muhonen, Anu MuhonenSearch for more papers by this authorJaspreet Kaur Takhi, Jaspreet Kaur TakhiSearch for more papers by this author Angela Creese, Angela CreeseSearch for more papers by this authorAdrian Blackledge, Adrian BlackledgeSearch for more papers by this authorArvind Bhatt, Arvind BhattSearch for more papers by this authorCarla Jonsson, Carla JonssonSearch for more papers by this authorKasper Juffermans, Kasper JuffermansSearch for more papers by this authorJinling Li, Jinling LiSearch for more papers by this authorPeter Martin, Peter MartinSearch for more papers by this authorAnu Muhonen, Anu MuhonenSearch for more papers by this authorJaspreet Kaur Takhi, Jaspreet Kaur TakhiSearch for more papers by this author Book Editor(s):Wayne E. Wright, Wayne E. WrightSearch for more papers by this authorSovicheth Boun, Sovicheth BounSearch for more papers by this authorOfelia García, Ofelia GarcíaSearch for more papers by this author First published: 24 April 2015 https://doi.org/10.1002/9781118533406.ch8Citations: 1 AboutPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShareShare a linkShare onFacebookTwitterLinked InRedditWechat Summary This chapter provides an opportunity to deconstruct the reflexive accounts researchers provide about their bilingualism. It describes how researchers wrote vignettes to discuss their role in the research team, and their researcher identities. These vignettes became an invaluable resource in the understandings of bilingualism as a social construct. Researching multilingualism involves bringing into play different voices which are in a complex and dynamic relationship with one another. There are discourses about equality which clash with discourses about social hierarchies; there are also discourses about bilingualism and blurred boundaries, which run concurrently with ideologies about language separation, ethnicity, and the right to represent. In selecting particular extracts, the chapter focuses on how notions of "language" and "bilingualism" appear in the vignettes, and shape one's research on multilingualism. Citing Literature The Handbook of Bilingual and Multilingual Education RelatedInformation

In this paper, we obtain some common fixed point theorems for recently introduced notion of PD-operators on a set X equipped with the function F without using the triangle inequality besides relaxing symmetric condition. Our results extend the results of Pathak and Rai [Common fixed points for PD-operator pairs under relaxed conditions with applications, Journal of Computational and Applied Mathematics 239(1)(2013) 103-113], Hussain et al.[Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal.74(2011) 2133-2140], Bhatt et al.[Common Fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Non-linear analysis Theory, Methods and appl. 73(2010) 176-182] and several others.

In this paper, we obtain a common fixed point theorem by employing the notion of g -reciprocal continuity in probabilistic metric space. We demonstrate that g -reciprocal continuity ensures the existence of common fixed point under strict contractive conditions, which otherwise do not ensure the existence of fixed points.

In this paper, we use the concept of a w-distance to prove a common coupled fixed point theorem for a family of maps on a metric space. Our results unify, generalize and complement the comparable results from the current literature.

In this paper, we obtain some common fixed point theorems for recently introduced notion of D-operator on a set X equipped with the function F: X x X -> Delta(+) without using the triangle inequality besides relaxing symmetric condition. Our results extend the results of Pathak and Rai.

We obtain some fixed point theorems for JH-operators and occasionally weakly g-biased maps on a set X together with the function F:X×X→Δ without using the triangle inequality and without using the symmetric condition. Our results extend the results of Bhatt et al. (2010).

In this paper, we obtain a common fixed point theorem by employing the notion of g-reciprocal continuity in symmetric spaces. We demonstrate that g-reciprocal continuity ensures the existence of common fixed point under strict contractive conditions, which otherwise do not ensure the existence of fixed points.

In this paper, we obtain some fixed point theorems for occasion- ally weakly compatible mappings in cone metric space. Our results extends the result of A.Bhatt, et al.(A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal., 73(2010) 176-182). Mathematics Subject Classification: Primary: 47H10, 54H25

Here is cutting edge research on complementary schooling in Britain. The book brings together new and innovative language-focused research on complementary schools that serve the linguistic, cultural and social needs of a wide range of ethno-linguistic communities in Britain. It examines the language and literacy practices, the policy and curricular innovation that pertain in complementary schools in Britain today, and the experiences of the children who attend them. Complementary schools have been on the margins of educational policy as research sites in their own right but recently this has changed. Now recognized as 'safe spaces' in which young children can explore their identities, they are seen as central to policy initiatives for promoting the languages of Britain. This book picks up on the spate of recent research to explore: the range of language and literacy practices in complementary schools; their innovations in policy and curriculum; and, how the pupils, teachers and parents negotiate social identities and affiliations. The book demonstrates the importance of complementary schools in the lives and learning of bilingual pupils. Sites of Multilingualism is essential reading for researchers and students in the fields of bilingual education and bilingualism, sociolinguistics, sociology and anthropology. It will also be relevant to teachers and teacher educators in complementary and mainstream schools and also to policy makers.

In this paper, we obtain some common fixed point theorems for occasionally weakly compatible mappings on a set X together with the function d:X×X→[0,∞) without using the triangle inequality and assuming symmetry only on the set of points of coincidence.

Sociolinguists have long recognized that language is a social construct, and have found elusive any firm definition of what constitutes a language in relation to overlapping varieties. On the other hand, it is long established that language is recruited by nations, communities and individuals for its symbolic value and distinctiveness. Whereas the first of these positions views language as fluid and changing, with permeable boundaries, the second stresses the fixed, rigid nature of language. This paper describes how these two positions are played out in the multilingual contexts of four English cities, in complementary schools where young students learn Bengali, Cantonese, Gujarati, Mandarin, and Turkish. In the research reported here we observed a broad range of multilingual practices across a variety of settings in schools, and at the boundaries of school and home. From these practices we identify two seemingly contradictory positions in relation to participants’ bilingualism: an ideology which argues for ‘language separation’ and one in which ‘flexible bilingualism’ flourishes as a practice. These two positions can be said to illustrate the dynamic tension described in sociolinguistic research, which has often viewed language as fluid and overlapping, while at the same time acknowledging language as a social construct which demarcates and reifies identities. The paper looks at how students and teachers simultaneously lived both ‘separate’ and ‘flexible’ positions, and navigated between them interactively and discursively. Our analysis suggests that relations between ‘language’ and ‘ideology’ are far from straightforward for the young people and teachers in complementary schools. The heteroglossic reality of multilingual practice, with its flexible movement across and between ‘languages’, is underpinned by the social structures of which such interactions are a part.

om Abstract. In this paper we prove common fixed point theorems for a pair of occasionally weakly compatible maps in probabilistic semi - metric space. These results are extensions of the results which we have obtained on symmet- ric spaces (3).

Ethnography has typically been seen as a singular research journey in which the lone researcher engages in the study of a community. However, increasingly within the social sciences, ethnographic research takes place in teams. This article explores the processes of using fieldnotes to develop team ethnography in a study of Gujarati complementary schools in a diverse English city. Complementary schools are also known as supplementary, heritage and community language schools. They are voluntary, usually run by local communities, and outside the state education sector. The article looks at how fieldnotes are used by researchers to constitute a team, contest interpretations and produce nuanced accounts of complementary schools. For the purpose of this article, a set of fieldnotes has been selected and presented as a case study to illustrate the role fieldnotes played in the team. The article explores their iterative use by the four-member team to settle upon particular research themes. We consider the role fieldnotes played in the team's reaching contested but shared accounts of social and linguistic action in one particular complementary school.