Some Fixed Point Theorems In Menger Spaces And Applications
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Some Fixed Point Theorems in Menger Spaces and Applications
Author: Suneel Kumar
language: de
Publisher: LAP Lambert Academic Publishing
Release Date: 2012-04
Fixed Point Theory is a beautiful mixture of analysis (pure and applied), topology and geometry. Fixed point theorems give the conditions under which mappings (single or multivalued) have solutions. The fixed point theory in probabilistic metric spaces is useful in the study of existence of solutions of operator equations in probabilistic metric space and probabilistic functional analysis, which is a very dynamic area of mathematical research. The notion of a probabilistic metric space corresponds to the situations when we do not know exactly the distance between two points; we know only probabilities of possible values of this distance. This book contains six chapters. New fixed point theorems for contraction mappings, expansion mappings, probabilistic densifying mappings are obtained in Menger spaces. Also related fixed point theorems in Menger spaces and applications of fixed point theorems are studied. This book will help the researchers studying fixed point theory.
Fixed Point Theory in Probabilistic Metric Spaces
Author: O. Hadzic
language: en
Publisher: Springer Science & Business Media
Release Date: 2001-11-30
Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory. Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces. In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces. Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.
Applications of Fixed-Point Theorem
This contributed volume contains chapters on various fixed-point theorems, including those in metric, b-metric and partial metric spaces. The book addresses the need for rigorous analytical methods in optimization, computational mathematics and applied sciences. By offering innovative solutions through iterative schemes and contraction principles, it bridges the gap between abstract mathematical principles and practical problem-solving approaches. The concept of fixed points has deep mathematical significance, influencing both theoretical frameworks and real-world applications. The book highlights the applications of fixed-point theory, presenting fundamental concepts and modern advancements, in diverse fields such as traffic control systems, stock market analysis, iterative algorithms and differential equations.