Generalizations of some fixed point theorems in banach and metric spaces
- Niyitegeka, Jean Marie Vianney
- Authors: Niyitegeka, Jean Marie Vianney
- Date: 2015
- Subjects: Fixed point theory , Banach spaces , Mappings (Mathematics)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/5265 , vital:20828
- Description: A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.
- Full Text:
- Date Issued: 2015
- Authors: Niyitegeka, Jean Marie Vianney
- Date: 2015
- Subjects: Fixed point theory , Banach spaces , Mappings (Mathematics)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/5265 , vital:20828
- Description: A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.
- Full Text:
- Date Issued: 2015
Josephine Baker: a psychobiographical study
- Authors: Eckley, Shannon Rose
- Date: 2012
- Subjects: Adlerian psychology , Baker, Josephine , Psychology -- Biographical methods , Personality
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9865 , http://hdl.handle.net/10948/d1007850 , Adlerian psychology , Baker, Josephine , Psychology -- Biographical methods , Personality
- Description: Psychobiographies examine an entire full life, from birth to death, with the aim of understanding the psychological development of that life. Psychobiographical research is a qualitative method of research, and is done by the use of both biography, and the application of relevant psychological theory. While the scientific merit of this type of research continues to be questioned and debated, interest in this area of research continues to grow on both a national, and international level. This particular research study aimed to explore the extraordinary and inspiring life of slave, dancer, singer, lover, soldier and mother, Josephine Baker (1906 – 1975), by applying Alfred Adler’s (1929) theory of personality namely, Individual Psychology. Josephine Baker was chosen by means of purposive sampling. The research study made use of a qualitative psychobiographical research method, which aimed to explore and describe the lived life and personality development of Josephine Baker, in terms of Alfred Adler’s (1929) theory of Individual Psychology. The data collection for this research study made use of a framework, as a means of selecting relevant data which formed a matrix, which in turn became a descriptive framework to organise and integrate the data (see Appendix A). The analysis thereof was done by the means of analytic generalisation (Yin, 1994). To assist in identifying salient data, analytical criteria namely, Alexander’s (1988) guidelines for the extraction of salient data were utilised (see Appendix B). This model also assisted in ensuring an accurate and complete description of Josephine Baker’s life in relation to the psychological theory used namely Alfred Adler’s theory of Individual Psychology. The findings of the study indicate that Josephine’s life paralleled Adler’s (1929) theory in many ways, and also indicated that the person she became was also strongly influenced by many familial, social, historical and cultural events of the time. This study has therefore shown that to date, there is still great value and relevance in Adler’s (1929) theory of Individual Psychology, even though it was proposed and developed almost a century ago. Consequently, recommendations regarding further psychiobiographical research in this area in the future have been made.
- Full Text:
- Date Issued: 2012
- Authors: Eckley, Shannon Rose
- Date: 2012
- Subjects: Adlerian psychology , Baker, Josephine , Psychology -- Biographical methods , Personality
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9865 , http://hdl.handle.net/10948/d1007850 , Adlerian psychology , Baker, Josephine , Psychology -- Biographical methods , Personality
- Description: Psychobiographies examine an entire full life, from birth to death, with the aim of understanding the psychological development of that life. Psychobiographical research is a qualitative method of research, and is done by the use of both biography, and the application of relevant psychological theory. While the scientific merit of this type of research continues to be questioned and debated, interest in this area of research continues to grow on both a national, and international level. This particular research study aimed to explore the extraordinary and inspiring life of slave, dancer, singer, lover, soldier and mother, Josephine Baker (1906 – 1975), by applying Alfred Adler’s (1929) theory of personality namely, Individual Psychology. Josephine Baker was chosen by means of purposive sampling. The research study made use of a qualitative psychobiographical research method, which aimed to explore and describe the lived life and personality development of Josephine Baker, in terms of Alfred Adler’s (1929) theory of Individual Psychology. The data collection for this research study made use of a framework, as a means of selecting relevant data which formed a matrix, which in turn became a descriptive framework to organise and integrate the data (see Appendix A). The analysis thereof was done by the means of analytic generalisation (Yin, 1994). To assist in identifying salient data, analytical criteria namely, Alexander’s (1988) guidelines for the extraction of salient data were utilised (see Appendix B). This model also assisted in ensuring an accurate and complete description of Josephine Baker’s life in relation to the psychological theory used namely Alfred Adler’s theory of Individual Psychology. The findings of the study indicate that Josephine’s life paralleled Adler’s (1929) theory in many ways, and also indicated that the person she became was also strongly influenced by many familial, social, historical and cultural events of the time. This study has therefore shown that to date, there is still great value and relevance in Adler’s (1929) theory of Individual Psychology, even though it was proposed and developed almost a century ago. Consequently, recommendations regarding further psychiobiographical research in this area in the future have been made.
- Full Text:
- Date Issued: 2012
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