商品描述
This book demonstrates the significance, applicability, and widespread nature of fixed point theorems in contexts outside of mathematics, including engineering, computer science, economics, and biological sciences. In the real world, fixed point theory is used to solve problems where stability, balance, or repeated processes are involved, such as predicting economic equilibrium, optimizing traffic flow, ensuring robots move precisely, or stabilizing medical devices like pacemakers. It is also used in artificial intelligence, engineering systems, and biological modeling where stable solutions in complex systems are needed. The authors not only highlight modern hurdles, but also explore how the field has accommodated and grown in response to them. The book provides comprehensive coverage of both the classical underpinnings and the cutting-edge advancements in fixed point theory. Each concept is illustrated with well-crafted, original examples that are carefully chosen to demonstrate both theoretical depth and practical significance. The chapters conclude with open problems and future research directions, encouraging further exploration. This book is designed to serve as both a guide for those entering the field as well as a resource for seasoned researchers looking to deepen their understanding of its modern applications.
商品描述(中文翻譯)
本書展示了不僅限於數學領域的固定點定理的重要性、適用性及其廣泛性，包括工程學、計算機科學、經濟學和生物科學等領域。在現實世界中，固定點理論用於解決涉及穩定性、平衡或重複過程的問題，例如預測經濟均衡、優化交通流量、確保機器人精確移動，或穩定像心臟起搏器這樣的醫療設備。它也應用於人工智慧、工程系統和生物建模中，這些領域需要在複雜系統中找到穩定解。作者不僅強調了現代的挑戰，還探討了該領域如何適應並在面對這些挑戰時成長。本書全面涵蓋了固定點理論的經典基礎和前沿進展。每個概念都配有精心設計的原創範例，這些範例經過仔細挑選，以展示理論深度和實際意義。各章節以開放性問題和未來研究方向作結，鼓勵進一步探索。本書旨在作為進入該領域的指南，同時也是希望加深對其現代應用理解的資深研究人員的資源。
作者簡介
Sumati Kumari Panda, Ph.D., is a Professor of Mathematics at the GMR Institute of Technology, India. Her research areas include fractional calculus, fixed point theory, neural networks, and their applications. She has published more than 100 research papers in reputed international journals and presented her work at several national and international conferences. She is currently serving as an Academic Editor for Scientific Reports (Springer, Scopus & SCIE-indexed). Dr. Panda received her Ph.D. in Mathematics from K.L. University in 2015. Velusamy Vijayakumar, Ph.D., is an Assistant Professor at the Vellore Institute of Technology (VIT), Vellore, India. His research interests include fractional calculus, dynamical systems, mathematical control theory, and neural networks. Dr. Vijayakumar has authored over 220 research articles in reputed scientific journals. Dr. Vijayakumar received his B.Sc, M.Sc, M.Phil, and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, Tamil Nadu, India, in 2002, 2004, 2006, and 2016 respectively. Ravi P. Agarwal, Ph.D., is an Emeritus Research Professor in the Department of Mathematics and Systems Engineering at the Florida Institute of Technology (USA). He has authored or co-authored more than 50 books and more than 2,000 research articles. He has received numerus honors and awards from several universities of the world. His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities. Dr. Agarwal received his Ph.D. at the Indian Institute of Technology, Madras, India, in 1973.
作者簡介(中文翻譯)
Sumati Kumari Panda 博士是印度 GMR 技術學院的數學教授。她的研究領域包括分數微積分、固定點理論、神經網絡及其應用。她在多個知名國際期刊上發表了超過 100 篇研究論文，並在多個國內外會議上展示她的研究成果。她目前擔任《Scientific Reports》（Springer，Scopus 和 SCIE 索引）的學術編輯。Panda 博士於 2015 年在 K.L. 大學獲得數學博士學位。
Velusamy Vijayakumar 博士是印度 Vellore 技術學院（VIT）的助理教授。他的研究興趣包括分數微積分、動態系統、數學控制理論和神經網絡。Vijayakumar 博士在多個知名科學期刊上發表了超過 220 篇研究文章。他於 2002、2004、2006 和 2016 年分別在印度泰米爾納德邦的 Bharathiar 大學獲得數學學士、碩士、哲學碩士和博士學位。
Ravi P. Agarwal 博士是美國佛羅里達科技學院數學與系統工程系的名譽研究教授。他著作或合著了超過 50 本書籍和 2000 多篇研究文章。他曾獲得來自世界多所大學的多項榮譽和獎項。他的研究興趣包括非線性分析、微分方程和差分方程、固定點理論以及一般不等式。Agarwal 博士於 1973 年在印度理工學院馬德拉斯校區獲得博士學位。
