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This book collects papers on major topics in fixed point theory and
its applications. Each chapter is accompanied by basic notions,
mathematical preliminaries and proofs of the main results. The book
discusses common fixed point theory, convergence theorems, split
variational inclusion problems and fixed point problems for
asymptotically nonexpansive semigroups; fixed point property and
almost fixed point property in digital spaces, nonexpansive
semigroups over CAT( ) spaces, measures of noncompactness, integral
equations, the study of fixed points that are zeros of a given
function, best proximity point theory, monotone mappings in modular
function spaces, fuzzy contractive mappings, ordered hyperbolic
metric spaces, generalized contractions in b-metric spaces,
multi-tupled fixed points, functional equations in dynamic
programming and Picard operators. This book addresses the
mathematical community working with methods and tools of nonlinear
analysis. It also serves as a reference, source for examples and
new approaches associated with fixed point theory and its
applications for a wide audience including graduate students and
researchers.
This book collects papers on major topics in fixed point theory and
its applications. Each chapter is accompanied by basic notions,
mathematical preliminaries and proofs of the main results. The book
discusses common fixed point theory, convergence theorems, split
variational inclusion problems and fixed point problems for
asymptotically nonexpansive semigroups; fixed point property and
almost fixed point property in digital spaces, nonexpansive
semigroups over CAT( ) spaces, measures of noncompactness, integral
equations, the study of fixed points that are zeros of a given
function, best proximity point theory, monotone mappings in modular
function spaces, fuzzy contractive mappings, ordered hyperbolic
metric spaces, generalized contractions in b-metric spaces,
multi-tupled fixed points, functional equations in dynamic
programming and Picard operators. This book addresses the
mathematical community working with methods and tools of nonlinear
analysis. It also serves as a reference, source for examples and
new approaches associated with fixed point theory and its
applications for a wide audience including graduate students and
researchers.
This book is a collection of original research and survey articles
on mathematical inequalities and their numerous applications in
diverse areas of mathematics and engineering. It includes chapters
on convexity and related concepts; inequalities for mean values,
sums, functions, operators, functionals, integrals and their
applications in various branches of mathematics and related
sciences; fractional integral inequalities; and weighted type
integral inequalities. It also presents their wide applications in
biomathematics, boundary value problems, mechanics, queuing models,
scattering, and geomechanics in a concise, but easily
understandable way that makes the further ramifications and future
directions clear. The broad scope and high quality of the
contributions make this book highly attractive for graduates,
postgraduates and researchers. All the contributing authors are
leading international academics, scientists, researchers and
scholars.
This book provides a detailed study of recent results in metric
fixed point theory and presents several applications in nonlinear
analysis, including matrix equations, integral equations and
polynomial approximations. Each chapter is accompanied by basic
definitions, mathematical preliminaries and proof of the main
results. Divided into ten chapters, it discusses topics such as the
Banach contraction principle and its converse; Ran-Reurings fixed
point theorem with applications; the existence of fixed points for
the class of - contractive mappings with applications to quadratic
integral equations; recent results on fixed point theory for cyclic
mappings with applications to the study of functional equations;
the generalization of the Banach fixed point theorem on Branciari
metric spaces; the existence of fixed points for a certain class of
mappings satisfying an implicit contraction; fixed point results
for a class of mappings satisfying a certain contraction involving
extended simulation functions; the solvability of a coupled fixed
point problem under a finite number of equality constraints; the
concept of generalized metric spaces, for which the authors extend
some well-known fixed point results; and a new fixed point theorem
that helps in establishing a Kelisky-Rivlin type result for
q-Bernstein polynomials and modified q-Bernstein polynomials. The
book is a valuable resource for a wide audience, including graduate
students and researchers.
This book provides a detailed study of recent results in metric
fixed point theory and presents several applications in nonlinear
analysis, including matrix equations, integral equations and
polynomial approximations. Each chapter is accompanied by basic
definitions, mathematical preliminaries and proof of the main
results. Divided into ten chapters, it discusses topics such as the
Banach contraction principle and its converse; Ran-Reurings fixed
point theorem with applications; the existence of fixed points for
the class of - contractive mappings with applications to quadratic
integral equations; recent results on fixed point theory for cyclic
mappings with applications to the study of functional equations;
the generalization of the Banach fixed point theorem on Branciari
metric spaces; the existence of fixed points for a certain class of
mappings satisfying an implicit contraction; fixed point results
for a class of mappings satisfying a certain contraction involving
extended simulation functions; the solvability of a coupled fixed
point problem under a finite number of equality constraints; the
concept of generalized metric spaces, for which the authors extend
some well-known fixed point results; and a new fixed point theorem
that helps in establishing a Kelisky-Rivlin type result for
q-Bernstein polynomials and modified q-Bernstein polynomials. The
book is a valuable resource for a wide audience, including graduate
students and researchers.
This book offers a comprehensive treatment of the theory of
measures of noncompactness. It discusses various applications of
the theory of measures of noncompactness, in particular, by
addressing the results and methods of fixed-point theory. The
concept of a measure of noncompactness is very useful for the
mathematical community working in nonlinear analysis. Both these
theories are especially useful in investigations connected with
differential equations, integral equations, functional integral
equations and optimization theory. Thus, one of the book's central
goals is to collect and present sufficient conditions for the
solvability of such equations. The results are established in
miscellaneous function spaces, and particular attention is paid to
fractional calculus.
This book offers a comprehensive treatment of the theory of
measures of noncompactness. It discusses various applications of
the theory of measures of noncompactness, in particular, by
addressing the results and methods of fixed-point theory. The
concept of a measure of noncompactness is very useful for the
mathematical community working in nonlinear analysis. Both these
theories are especially useful in investigations connected with
differential equations, integral equations, functional integral
equations and optimization theory. Thus, one of the book's central
goals is to collect and present sufficient conditions for the
solvability of such equations. The results are established in
miscellaneous function spaces, and particular attention is paid to
fractional calculus.
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