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Masters Degrees (Pure Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7121

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Browsing Masters Degrees (Pure Mathematics) by Subject "Banach spaces."

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    Iterative algorithms for approximating solutions of variational inequality problems and monotone inclusion problems.
    (2017) Chinedu, Izuchukwu.; Mewomo, Oluwatosin Temitope.
    In this work, we introduce and study an iterative algorithm independent of the operator norm for approximating a common solution of split equality variational inequality prob- lem and split equality xed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality variational inequality problem and the set of solutions of a split equality xed point problem for demicontractive mappings in real Hilbert spaces. We then considered nite families of split equality variational inequality problems and proposed an iterative algorithm for approximating a common solution of this problem and the multiple-sets split equality xed point problem for countable families of multivalued type-one demicontractive-type mappings in real Hilbert spaces. A strong convergence re- sult of the sequence generated by our proposed algorithm to a solution of this problem was also established. We further extend our study from the frame work of real Hilbert spaces to more general p-uniformly convex Banach spaces which are also uniformly smooth. In this space, we introduce an iterative algorithm and prove a strong convergence theorem for approximating a common solution of split equality monotone inclusion problem and split equality xed point problem for right Bregman strongly nonexpansive mappings. Finally, we presented numerical examples of our theorems and applied our results to study the convex minimization problems and equilibrium problems.
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    On amenability properties of some closed ideals of B(X)
    (2018) Buthelezi, Thabo Njabulo.; Mewomo, Oluwatosin Temitope.
    Abstract available in PDF file.
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    On pseudo-amenability of C(X;A) for norm irregular Banach algebra A.
    (2017) Adiele, Ugochukwu.; Mewomo, Oluwatosin Temitope.
    Abstract available in PDF file.
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    Self-adaptive inertial algorithms for approximating solutions of split feasilbility, monotone inclusion, variational inequality and fixed point problems.
    (2020) Owolabi, Abd-semii Oluwatosin-Enitan.; Mewomo, Oluwatosin Temitope.
    In this dissertation, we introduce a self-adaptive hybrid inertial algorithm for approximating a solution of split feasibility problem which also solves a monotone inclusion problem and a fixed point problem in p-uniformly convex and uniformly smooth Banach spaces. We prove a strong convergence theorem for the sequence generated by our algorithm which does not require a prior knowledge of the norm of the bounded linear operator. Numerical examples are given to compare the computational performance of our algorithm with other existing algorithms. Moreover, we present a new iterative algorithm of inertial form for solving Monotone Inclusion Problem (MIP) and common Fixed Point Problem (FPP) of a finite family of demimetric mappings in a real Hilbert space. Motivated by the Armijo line search technique, we incorporate the inertial technique to accelerate the convergence of the proposed method. Under standard and mild assumptions of monotonicity and Lipschitz continuity of the MIP associated mappings, we establish the strong convergence of the iterative algorithm. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with the non-inertial version and some related methods in the literature. Furthermore, we propose a new modified self-adaptive inertial subgradient extragradient algorithm in which the two projections are made onto some half spaces. Moreover, under mild conditions, we obtain a strong convergence of the sequence generated by our proposed algorithm for approximating a common solution of variational inequality problems and common fixed points of a finite family of demicontractive mappings in a real Hilbert space. The main advantages of our algorithm are: strong convergence result obtained without prior knowledge of the Lipschitz constant of the the related monotone operator, the two projections made onto some half-spaces and the inertial technique which speeds up rate of convergence. Finally, we present an application and a numerical example to illustrate the usefulness and applicability of our algorithm.
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    Some notions of amenability of Banach semigroup algebras.
    (2017) Adebayo, Mebawondu Akindele.; Mewomo, Oluwatosin Temitope.
    Abstract available in PDF file.