A Study on Fixed Point Theory

Fixed point theory is an attractive and interesting subject with a large number of applications in various fields of mathematics and other branches of science. Fixed point theory is divided into three major types : i) Topological Fixed Point Theory ii) Metric Fixed Point Theory iii) Order-Theoretic Fixed Point Theory. Fixed point theory has become not only a field with a huge development but also a very helpful means for solving various problems in different fields of mathematics. Fixed point theorems are used for proving the existence and uniqueness to differential, integral and partial differential equations and variational inequalities etc. Above all, they are also useful in the field of computer science, image processing, artificial intelligence, decision making, population dynamics, operational research, industrial engineering, pattern recognition, medicine, group health underwriting, management and many other fields. Only a few common selected applications are provided here.

Ph. S. Singh, Gold Medalist, M.Sc. Mathematics, University of Delhi, India is a researcher on the field of fixed point theory. He has written different papers on the topic. He had participated the MTTS Programme under NBHM, India successfully. He had received different scholarships/fellowships during his studies.