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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.

gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion

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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.

Research & information: general --- Mathematics & science --- 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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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.

Research & information: general --- Mathematics & science --- 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 --- 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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Metric fixed-point theory lies in the intersection of three main subjects: topology, functional analysis, and applied mathematics. The first fixed-point theorem, also known as contraction mapping principle, was abstracted by Banach from the papers of Liouville and Picard, in which certain differential equations were solved by using the method of successive approximation. In other words, fixed-point theory developed from applied mathematics and has developed in functional analysis and topology. Fixed-point theory is a dynamic research subject that has never lost the attention of researchers, as it is very open to development both in theoretical and practical fields. In this Special Issue, among several submissions, we selected eight papers that we believe will be interesting to researchers who study metric fixed-point theory and related applications. It is great to see that this Special Issue fulfilled its aims. There are not only theoretical results but also some applications that were based on obtained fixed-point results. In addition, the presented results have great potential to be improved, extended, and generalized in distinct ways. The published results also have a wide application potential in various qualitative sciences, including physics, economics, computer science, engineering, and so on.

b-metric --- Banach fixed point theorem --- Caristi fixed point theorem --- homotopy --- M-metric --- M-Pompeiu–Hausdorff type metric --- multivalued mapping --- fixed point --- quasi metric space --- altering distance function --- (ψ, ϕ)-quasi contraction. --- pata type contraction --- Suzuki type contraction --- C-condition --- orbital admissible mapping --- non-Archimedean quasi modular metric space --- θ-contraction --- Suzuki contraction --- simulation contraction --- R-function --- simulation function --- manageable function --- contractivity condition --- binary relation --- quasi-metric space --- left K-complete --- α–ψ-contractive mapping --- asymptotic stability --- differential and riemann-liouville fractional differential neutral systems --- linear matrix inequality

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The topic of this book is the mathematical and numerical analysis of some recent frameworks based on differential equations and their application in the mathematical modeling of complex systems, especially of living matter. First, the recent new mathematical frameworks based on generalized kinetic theory, fractional calculus, inverse theory, Schrödinger equation, and Cahn–Hilliard systems are presented and mathematically analyzed. Specifically, the well-posedness of the related Cauchy problems is investigated, stability analysis is also performed (including the possibility to have Hopf bifurcations), and some optimal control problems are presented. Second, this book is concerned with the derivation of specific models within the previous mentioned frameworks and for complex systems in biology, epidemics, and engineering. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of complex systems.

Research & information: general --- Mathematics & science --- boundedness --- delay --- Hopf bifurcation --- Lyapunov functional --- stability --- SEIQRS-V model --- kinetic theory --- integro-differential equations --- complex systems --- evolution equations --- thermostat --- nonequilibrium stationary states --- discrete Fourier transform --- discrete kinetic theory --- nonlinearity --- fractional operators --- Cahn–Hilliard systems --- well-posedness --- regularity --- optimal control --- necessary optimality conditions --- Schrödinger equation --- Davydov’s model --- partial differential equations --- exact solutions --- fractional derivative --- abstract Cauchy problem --- C0−semigroup --- inverse problem --- active particles --- autoimmune disease --- degenerate equations --- real activity variable --- Cauchy problem --- electric circuit equations --- wardoski contraction --- almost (s, q)—Jaggi-type --- b—metric-like spaces --- second-order differential equations --- dynamical systems --- compartment model --- epidemics --- basic reproduction number --- boundedness --- delay --- Hopf bifurcation --- Lyapunov functional --- stability --- SEIQRS-V model --- kinetic theory --- integro-differential equations --- complex systems --- evolution equations --- thermostat --- nonequilibrium stationary states --- discrete Fourier transform --- discrete kinetic theory --- nonlinearity --- fractional operators --- Cahn–Hilliard systems --- well-posedness --- regularity --- optimal control --- necessary optimality conditions --- Schrödinger equation --- Davydov’s model --- partial differential equations --- exact solutions --- fractional derivative --- abstract Cauchy problem --- C0−semigroup --- inverse problem --- active particles --- autoimmune disease --- degenerate equations --- real activity variable --- Cauchy problem --- electric circuit equations --- wardoski contraction --- almost (s, q)—Jaggi-type --- b—metric-like spaces --- second-order differential equations --- dynamical systems --- compartment model --- epidemics --- basic reproduction number