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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to reallife phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.
Legendre wavelets  collocation method  threestep Taylor method  asymptotic stability  timedependent partial differential equations  noninstantaneous impulses  Caputo fractional derivative  differential equations  state dependent delays  lipschitz stability  limitperiodic solutions  difference equations  exponential dichotomy  strong nonlinearities  effective existence criteria  population dynamics  discrete Lyapunov equation  difference equations  Hilbert space  dichotomy  exponential stability  ?Laplacian operator  mean curvature operator  heteroclinic solutions  problems in the real line  lower and upper solutions  Nagumo condition on the real line  fixed point theory  coupled nonlinear systems  functional boundary conditions  Schauder’s fixed point theory  Arzèla Ascoli theorem  lower and upper solutions  first order periodic systems  SIRS epidemic model  mathematical modelling  Navier–Stokes equations  global solutions  regular solutions  a priori estimates  weak solutions  kinetic energy  dissipation  Bäcklund transformation  Clairin’s method  generalized Liouville equation  Miura transformation  Kortewegde Vries equation  secondorder differential/difference/qdifference equation of hypergeometric type  nonuniform lattices  divideddifference equations  polynomial solution  integrodifferentials  Sumudu decomposition method  dynamical system
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.
analytic functions  starlike functions  convex functions  FeketeSzegö inequality  Hilbert C*module  gframe  gBessel sequence  adjointable operator  analytic functions  starlike functions  convex functions  FeketeSzegö inequality  operator inequality  positive linear map  operator Kantorovich inequality  geometrically convex function  frame  weaving frame  weaving frame operator  alternate dual frame  Hilbert space  quantum estimates  HermiteHadamard type inequalities  quasiconvex  Hermite–Hadamard type inequality  strongly ?convex functions  Hölder’s inequality  Power mean inequality  Katugampola fractional integrals  Riemann–Liouville fractional integrals  Hadamard fractional integrals  Steffensen’s inequality  higher order convexity  Green functions  Montgomery identity  Fink’s identity  HermiteHadamard inequality  intervalvalued functions  (h1, h2)convex  majorization inequality  twice differentiable convex functions  refined inequality  Taylor theorem  Gronwall–Bellman inequality  proportional fractional derivative  Riemann–Liouville and Caputo proportional fractional initial value problem  convex functions  Fejér’s inequality  special means  weaving frame  weaving Kframe  Kdual  pseudoinverse  ?variation  onesided singular integral  commutator  onesided weighted Morrey space  onesided weighted Campanato space  power inequalities  exponential inequalities  trigonometric inequalities  weight function  halfdiscrete HardyHilbert’s inequality  parameter  EulerMaclaurin summation formula  reverse inequality
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Computational intelligence is a general term for a class of algorithms designed by nature's wisdom and human intelligence. Computer scientists have proposed many computational intelligence algorithms with heuristic features. These algorithms either mimic the evolutionary processes of the biological world, mimic the physiological structure and bodily functions of the organism,
artificial bee colony algorithm (ABC)  cloud model  normal cloud model  Y conditional cloud generator  global optimum  evolution  computation  urban design  biology  shape grammar  architecture  SPEA 2  energyefficient job shop scheduling  dispatching rule  nonlinear convergence factor  mutation operation  whale optimization algorithm  particle swarm optimization  confidence term  random weight  benchmark functions  ttest  success rates  average iteration times  setunion knapsack problem  moth search algorithm  transfer function  discrete algorithm  evolutionary multiobjective optimization  convergence point  acceleration search  evolutionary computation  optimization  bat algorithm (BA)  bat algorithm with multiple strategy coupling (mixBA)  CEC2013 benchmarks  Wilcoxon test  Friedman test  facility layout design  single loop  monarch butterfly optimization  slicing tree structure  material handling path  integrated design  wireless sensor networks (WSNs)  DVHop algorithm  multiobjective DVHop localization algorithm  NSGAIIDVHop  firstarrival picking  fuzzy cmeans  particle swarm optimization  range detection  minimum total dominating set  evolutionary algorithm  genetic algorithm  local search  constrained optimization problems (COPs)  evolutionary algorithms (EAs)  firefly algorithm (FA)  stochastic ranking (SR)  Artificial bee colony  swarm intelligence  elite strategy  dimension learning  global optimization  DE algorithm  ?Hilbert space  topology structure  quantum uncertainty property  numerical simulation  whale optimization algorithm  flexible job shop scheduling problem  nonlinear convergence factor  adaptive weight  variable neighborhood search  elephant herding optimization  EHO  swarm intelligence  individual updating strategy  largescale  benchmark  diversity maintenance  particle swarm optimizer  entropy  large scale optimization  minimum load coloring  memetic algorithm  evolutionary  local search  particle swarm optimization  largescale optimization  adaptive multiswarm  diversity maintenance  deep learning  convolutional neural network  rock types  automatic identification  monarch butterfly optimization  greedy optimization algorithm  global position updating operator  01 knapsack problems
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a nontrivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
point projection  intersection  parametric curve  ndimensional Euclidean space  Newton’s second order method  fixed point theorem  nonlinear equations  multiple zeros  optimal iterative methods  higher order of convergence  nonlinear operator equation  Fréchet derivative  ?continuity condition  Newtonlike method  Frédholm integral equation  nonlinear equations  Padé approximation  iterative method  order of convergence  numerical experiment  fourth order iterative methods  local convergence  banach space  radius of convergence  nonlinear equation  iterative process  nondifferentiable operator  Lipschitz condition  high order  sixteenth order convergence method  local convergence  dynamics  Banach space  Newton’s method  semilocal convergence  Kantorovich hypothesis  iterative methods  Steffensen’s method  Rorder  with memory  computational efficiency  nonlinear equation  basins of attraction  optimal order  higher order method  computational order of convergence  nonlinear equations  multiple roots  Chebyshev–Halleytype  optimal iterative methods  efficiency index  Banach space  semilocal convergence  ?continuity condition  Jarratt method  error bound  Fredholm integral equation  Newton’s method  global convergence  variational inequality problem  split variational inclusion problem  multivalued quasinonexpasive mappings  Hilbert space  sixteenthorder optimal convergence  multipleroot finder  asymptotic error constant  weight function  purely imaginary extraneous fixed point  attractor basin  drazin inverse  generalized inverse  iterative methods  higher order  efficiency index  integral equation  efficiency index  nonlinear models  iterative methods  higher order  nonlinear equations  optimal iterative methods  multiple roots  efficiency index  iterative methods  nonlinear equations  Newtontype methods  smooth and nonsmooth operators  heston model  Hull–White  option pricing  PDE  finite difference (FD)  iteration scheme  Moore–Penrose  rectangular matrices  rate of convergence  efficiency index  nonlinear equations  conjugate gradient method  projection method  convex constraints  signal and image processing  nonlinear monotone equations  conjugate gradient method  projection method  signal processing  nonlinear systems  multipoint iterative methods  divided difference operator  order of convergence  Newton’s method  computational efficiency index  system of nonlinear equations  Newton method  NewtonHSS method  nonlinear HSSlike method  PicardHSS method  convexity  least square problem  accretive operators  signal processing  point projection  intersection  planar algebraic curve  Newton’s iterative method  the improved curvature circle algorithm  systems of nonlinear equations  King’s family  order of convergence  multipoint iterative methods  nonlinear equations  Potra–Pták method  optimal methods  weight function  basin of attraction  engineering applications  Kung–Traub conjecture  multipoint iterations  nonlinear equation  optimal order  basins of attraction
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