In this thesis, we study multivalued monotone operators in Hadamard spaces and introduce a new mapping given by a nite family of these operators. We propose a modied Halpern-type algorithm for this mapping and prove that the algorithm converges strongly to a common solution of a nite family of monotone inclusion problems and xed point problem for a nonexpansive mapping in Hadamard spaces. Furthermore, we study some viscosity approximation techniques for approximating a common solution of a nite family of monotone inclusion problems and xed point problem for nonexpansive mapping, which is also a unique solution of some variational inequality problems in Hadamard spaces. More so, we propose and study some viscosity-type proximal point algorithms for approximating a common solution of minimization problem and xed point problem for nonexpansive multivalued mappings, which is also a unique solution of some variational inequality problems in Hadamard spaces. We then progress to propose some iterative algorithms for approximating a common solution of a nite family of minimization, monotone inclusion and xed point problems for demicontractive-type mappings in Hadamard spaces. In addition, we study equilibrium problems in Hadamard spaces and propose some viscosity-type proximal point algorithms, comprising of a nonexpansive mapping and resolvents of monotone bifunctions. We then prove that the proposed algorithms converge strongly to a common solution of a nite family of equilibrium problems in Hadamard spaces. To generalize the study of equilibrium problems in Hadamard spaces, we introduce a new optimization problem in Hadamard spaces, called the mixed equilibrium problem, and establish the existence of solutions for this problem in Hadamard spaces. We then analyze the asymptotic behavior of the sequence generated by a certain proximal point algorithm for this new optimization problem in Hadamard spaces. We also introduce and study a new class of mappings called the generalized strictly pseudononspreading mappings in Hadamard spaces. We then propose a Mann and Ishikawa-type algorithms for this class of mappings and prove that both algorithms converge strongly to a xed point of the generalized strictly pseudononspreading mapping. More so, we propose an S-type iteration and a viscositytype iteration for approximating a xed point of this mapping, which is also a solution of minimization and monotone inclusion problems in Hadamard spaces. To further generalize the study of optimization and xed point problems, we study the concept of minimization and xed point problems for nonexpansive mappings in geodesic metric spaces more general than Hadamard spaces, namely, the p-uniformly convex metric spaces. We introduce the concept of split minimization problems in p-uniformly convex metric spaces and study both Mann and Halpern proximal point algorithms for solving these problems in these spaces. Furthermore, we introduce the classes of asymptotically demicontractive multivalued mappings in Hadamard space, strict asymptotically pseudocontractive-type mappings in p-uniformly convex metric space and generalized strictly pseudononspreading mappings in p-uniformly convex metric spaces. Moreover, we propose several iterative algorithms for approximating a common xed point of nite family of these mappings. As application of the above study, we solve variational inequality problems and convex feasibility problems in Hadamard spaces. More so, we give several nontrival numerical examples of our results. Using these examples, we carry out various numerical experiments of these results in comparison with other important existing results in the literature. The results of the numerical experiments show that our theoretical results have competitive advantages over existing results in the literature. In some cases, we see that these numerical results are not applicable in Hilbert and Banach spaces. This means that, established results concerning optimization and xed point problems in these spaces (Hilbert and Banach) cannot be applied to such examples. Finally, some open problems regarding our results are identied and discussed, which oer many opportunities for future research.

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