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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.
This is an eclectic tome of 100 papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory,information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics ¿ containing 800 pages.It was my preoccupation and collaboration as author, co-author, translator, or co-translator, and editor with many scientists from around the world for long time. Many ideas from this book are to be developed and expanded in future explorations.
This album of tehno-art represents the complements of ex-centric mathematics, which, reunited with the ordinary mathematics, have been temporarily named supermathematics. It has been named this way because it generates the multiplication, from one to infinite, of all functions, curves, relations, etc., in other words of all actual mathematics? entities. The supermathematics has the same equation for circle as for perfect square or triangles. In supermathematics there is no difference between linear and nonlinear. And, also, as it can be observed from this album, it gets, sometimes, ?artistic? valences. And this is just a small human step in mathematics and a big leap of mathematics for the mankind.The preparation of this album was made possible only because of the discovery of the mathematics? complements. The mathematical expressions of the new supermathematics functions constitute the base of the colored curves? families, as well as the base of some technical and/or artistic solids.
This book pinpoints the impact of new technologies on language and communication, highlights the evolution and changes undergone by humanities in conjunction with technological innovation, and looks at how language has adapted to the challenges of today’s digitized world.