Recent Developments in Fixed-Point Theory

Mudasir Younis is a postdoctoral research fellow at the Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Uttar Pradesh, India. For the last five years of his considerable research, he has been researching diverse fixed-point theorems within the graph structure of metric spaces, which is a relatively fresh addition to the relevant topic. In this context, he obtained several novel results and worked on determining the existence of solutions to various real-world engineering science and physics problems, such as a damped spring-mass system, deformation of an elastic beam, vibrations of a vertical heavy hanging cable, ascending motion of a rocket, tuning circuit problem, and so on. With more than 25 research papers published in SCI/ESCI/Scopus-listed journals and seven other papers communicated to prestigious international publications, he has received fellowships at both the national and international levels. Lili Chen is an Academic Professor and Doctorate Supervisor at the College of Mathematics and System Science at Shandong University of Science and Technology, Qingdao, China. In recent years, she has been primarily involved in research on the geometry theory of Banach spaces and fixed-point theory and its applications. She is a commentator of the American Mathematical Review, a member of the Chinese Mathematical Society and a member of the American Mathematical Society. She is a reviewer for several international SCI academic journals and has also supervised 8 projects. She has over 30 papers published in peer-reviewed SCI journals. She has so far supervised 14 graduate students and two doctoral students. Deepak Singh is Associate Professor of Mathematics at the Department of Applied Sciences, National Institute of Technical Teachers’ Training and Research, Bhopal India. He earned his M.Sc. and Ph.D. degrees in Mathematics from Barkatullah University, Bhopal. With more than 22 years of teaching experience, he has taught various courses in pure mathematics, applied mathematics and computer applications at undergraduate and at graduate levels. With more than 60 research papers to his credit, many of them are published in various SCI/ISI/Scopus/ESCI, Springer and Elsevier journals, he has supervised 15 Ph.D. students and 21 M.Phil. projects. Besides, he keeps participating in various scientific meetings, conferences in India and abroad. So far, he has delivered over 40 contributed and invited talks including 17 in the European and Asian countries. He is a reviewer of the American Mathematical Society and also a referee of many SCI/Springer/Elsevier journals.

Chapter 1 ​A Careful Retrospection of Metric Spaces and Contraction Mappings with Computer Simulation.- Chapter 2 Fixed-Point Theory for Multi-valued Feng–Liu Operators in Vector-Valued Metric Spaces.- Chapter 3 Iterative Algorithms for the Split Equality Problem.- Chapter 4 Some Fixed-Point Theorems of Generalized Contractions with Application to Boundary-Value Problem.- Chapter 5 Fixed Points of Coset and Orbit Space Actions: An Application of Semihypergroup Theory.