Mathematical Analysis in Interdisciplinary Research

This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.

這本專著提供了廣泛的數學分析研究和說明性論文，涵蓋了各種領域的應用。書中呈現了眾多主題的最新知識，對於理論和應用的跨學科研究的研究生和研究人員非常有用。重點包括：最佳控制問題、通信網絡最佳維護、帶有不確定性的最佳緊急疏散、合作和非合作的偏微分系統、變分不等式和一般均衡模型、各向異性彈性和調和函數、非線性隨機微分方程、算子方程、Kantorovich型的最大乘積算子、算子的擾動、積分算子、涉及最大單調算子的動力系統、三體問題、欺騙性系統、雙曲方程、強廣義預凸函數、迪利克雷字符、概率分佈函數、應用統計、積分不等式、廣義凸性、時空的全局雙曲性、道格拉斯-拉奇福德方法、不動點問題、一般羅德里格斯問題、巴拿赫代數、仿射群、吉布斯半群、關聯空間、稀疏數據表示、Meier-Keeler順序收縮、混合收縮和多項式方程。本書中的一些作品還提供了進一步研究的指南，以及對新方向和開放問題的建議。

Ioannis N. Parasidis received a Ph.D. in mathematical analysis from Kazakh State University in Kazakhstan in 1989. He worked in the Kazakh State University until 1994 and he is now a professor in the University of Thessaly in Greece. His research interests are extensions of operators, boundary value problems for differential, integro-differential and loaded equations, spectral and inverse problems, and difference equations.
Efthimios Providas received a Ph.D. in numerical analysis from Brunel University in UK in 1990. He is an associate professor in the University of Thessaly in Greece. His expertise includes applied mathematics, numerical analysis, finite element methods and boundary value problems for differential, integro-differential, loaded and difference equations. Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 47 (in 2021).

Ioannis N. Parasidis於1989年在哈薩克斯坦的哈薩克國立大學獲得數學分析博士學位。他在哈薩克國立大學工作到1994年，現在是希臘塞薩利大學的教授。他的研究興趣包括算子擴展、微分、積分微分和加載方程的邊界值問題、光譜和反問題，以及差分方程。

Efthimios Providas於1990年在英國布魯內爾大學獲得數值分析博士學位。他是希臘塞薩利大學的副教授。他的專業領域包括應用數學、數值分析、有限元方法以及微分、積分微分、加載和差分方程的邊界值問題。

Themistocles M. Rassias是雅典國立技術大學的數學教授。他的研究興趣包括非線性分析、全局分析、逼近理論、泛函分析、泛函方程、不等式及其應用。Rassias教授於1976年從加州大學伯克利分校獲得數學博士學位，他的博士論文指導教授是Stephen Smale，學術指導教授是Shiing-Shen Chern。除了大量的期刊發表之外，Rassias教授還與Springer出版社合作出版了幾本書籍，並擔任多個數學分析和優化領域期刊的編輯委員會成員。他的著作獲得了大量引用，h指數為47（截至2021年）。