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Fixed Point Theory and its Applications to Real World Problems (Hardcover)
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Fixed Point Theory and its Applications to Real World Problems (Hardcover)
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Fixed-point theory initially emerged in the article demonstrating
existence of solutions of differential equations, which appeared in
the second quarter of the 18th century (Joseph Liouville, 1837).
Later on, this technique was improved as a method of successive
approximations (Charles Emile Picard, 1890) which was extracted and
abstracted as a fixed-point theorem in the framework of complete
normed space (Stefan Banach, 1922). It ensures presence as well as
uniqueness of a fixed point, gives an approximate technique to
really locate the fixed point and the a priori and a posteriori
estimates for the rate of convergence. It is an essential device in
the theory of metric spaces. Subsequently, it is stated that
fixed-point theory is initiated by Stefan Banach. Fixed-point
theorems give adequate conditions under which there exists a fixed
point for a given function and enable us to ensure the existence of
a solution of the original problem. In an extensive variety of
scientific issues, beginning from different branches of
mathematics, the existence of a solution is comparable to the
existence of a fixed point for a suitable mapping. The book "Fixed
Point Theory & its Applications to Real World Problems" is an
endeavour to present results in fixed point theory which are
extensions, improvements and generalizations of classical and
recent results in this area and touches on distinct research
directions within the metric fixed-point theory. It provides new
openings for further exploration and makes for an easily accessible
source of knowledge. This book is apposite for young researchers
who want to pursue their research in fixed-point theory and is the
latest in the field, giving new techniques for the existence of a
superior fixed point, a fixed point, a near fixed point, a fixed
circle, a near fixed interval circle, a fixed disc, a near fixed
interval disc, a coincidence point, a common fixed point, a coupled
common fixed point, amiable fixed sets, strong coupled fixed points
and so on, utilizing minimal conditions. It offers novel
applications besides traditional applications which are applicable
to real world problems. The book is self-contained and unified
which will serve as a reference book to researchers who are in
search of novel ideas. It will be a valued addition to the library.
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