New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory.Topics include:Fixed point theoryFixed-circle theoryCoupled fixed pointsNonlinear duality in Banach spacesJensen's integral inequality and applicationsNonlinear differential equationsNonlinear integro-differential equationsQuasiconvexity, Stability of a Cauchy-Jensen additive mappingGeneralizations of metric spacesHilbert-type integral inequality, SolitonsQuadratic functional equations in fuzzy Banach spacesAsymptotic orbits in Hill’sproblemTime-domain electromagneticsInertial Mann algorithmsMathematical modellingRoboticsGraduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.