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In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.

common coupled fixed point --- bv(s)-metric space --- T-contraction --- weakly compatible mapping --- quasi-pseudometric --- start-point --- end-point --- fixed point --- weakly contractive --- variational inequalities --- inverse strongly monotone mappings --- demicontractive mappings --- fixed point problems --- Hadamard spaces --- geodesic space --- convex minimization problem --- resolvent --- common fixed point --- iterative scheme --- split feasibility problem --- null point problem --- generalized mixed equilibrium problem --- monotone mapping --- strong convergence --- Hilbert space --- the condition (ℰμ) --- standard three-step iteration algorithm --- uniformly convex Busemann space --- compatible maps --- common fixed points --- convex metric spaces --- q-starshaped --- fixed-point --- multivalued maps --- F-contraction --- directed graph --- metric space --- coupled fixed points --- cyclic maps --- uniformly convex Banach space --- error estimate --- equilibrium --- fixed points --- symmetric spaces --- binary relations --- T-transitivity --- regular spaces --- b-metric space --- b-metric-like spaces --- Cauchy sequence --- pre-metric space --- triangle inequality --- weakly uniformly strict contraction --- S-type tricyclic contraction --- metric spaces --- b2-metric space --- binary relation --- almost ℛg-Geraghty type contraction

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Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.

Differential dynamical systems --- Drie-menigvuldigheden (Topologie) --- Three-manifolds (Topology) --- Trois-variétés (Topologie) --- Differentiable dynamical systems. --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Low-dimensional topology --- Topological manifolds --- Algebraic topology. --- Analytic continuation. --- Automorphism. --- Beltrami equation. --- Bifurcation theory. --- Boundary (topology). --- Cantor set. --- Circular symmetry. --- Combinatorics. --- Compact space. --- Complex conjugate. --- Complex manifold. --- Complex number. --- Complex plane. --- Conformal geometry. --- Conformal map. --- Conjugacy class. --- Convex hull. --- Covering space. --- Deformation theory. --- Degeneracy (mathematics). --- Dimension (vector space). --- Disk (mathematics). --- Dynamical system. --- Eigenvalues and eigenvectors. --- Factorization. --- Fiber bundle. --- Fuchsian group. --- Fundamental domain. --- Fundamental group. --- Fundamental solution. --- G-module. --- Geodesic. --- Geometry. --- Harmonic analysis. --- Hausdorff dimension. --- Homeomorphism. --- Homotopy. --- Hyperbolic 3-manifold. --- Hyperbolic geometry. --- Hyperbolic manifold. --- Hyperbolic space. --- Hypersurface. --- Infimum and supremum. --- Injective function. --- Intersection (set theory). --- Invariant subspace. --- Isometry. --- Julia set. --- Kleinian group. --- Laplace's equation. --- Lebesgue measure. --- Lie algebra. --- Limit point. --- Limit set. --- Linear map. --- Mandelbrot set. --- Manifold. --- Mapping class group. --- Measure (mathematics). --- Moduli (physics). --- Moduli space. --- Modulus of continuity. --- Möbius transformation. --- N-sphere. --- Newton's method. --- Permutation. --- Point at infinity. --- Polynomial. --- Quadratic function. --- Quasi-isometry. --- Quasiconformal mapping. --- Quasisymmetric function. --- Quotient space (topology). --- Radon–Nikodym theorem. --- Renormalization. --- Representation of a Lie group. --- Representation theory. --- Riemann sphere. --- Riemann surface. --- Riemannian manifold. --- Schwarz lemma. --- Simply connected space. --- Special case. --- Submanifold. --- Subsequence. --- Support (mathematics). --- Tangent space. --- Teichmüller space. --- Theorem. --- Topology of uniform convergence. --- Topology. --- Trace (linear algebra). --- Transversal (geometry). --- Transversality (mathematics). --- Triangle inequality. --- Unit disk. --- Unit sphere. --- Upper and lower bounds. --- Vector field. --- Differentiable dynamical systems --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds