Browsing by Author "Usamot, I. F."

Now showing 1 - 5 of 5
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    Common Coupled Fixed Point Theorems without Compatibility in Partially Ordered Metric Spaces
    (International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2022-06-30) Tijani, K. R.; Wahab, O. T.; Usamot, I. F.; Alata, S. M.
    A perfect blend of requirements for the proof of common coupled fixed point theorems in partially ordered metric space without the assumptions of (weak) compatibility is accomplished. Previous attempts in this direction involving these assumptions mostly ensure existence of coupled coincidence points. In many existing works in this area, attempt have been made to prove the existence of common coupled fixed points. However, only identity mappings can satisfy the conditions of the theorems. The method of proof presented in this present work is powerful in view of the fact that it guarantees the existence of common coupled fixed points without the imposition of (weak) compatibility conditions and identity mappings. To illustrate the results, an example is provided.
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    Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces
    (Hindawi Publishing Corporation, 2016-09-09) Wahab, O. T.; Olawuyi, R. O.; RAUF, K.; Usamot, I. F.
    This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that S-iteration converges faster than other iterations followed by Picard-Mann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among two-step iterative fixed point schemes in the literature.
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    Green’s Equivalence Classes in Full Transformation Semigroups: A Height-based Approach
    (Department of Mathematics, Universitas Negeri Gorontalo, Indonesia, 2025-04-08) Usamot, I. F.; Ibrahim, G.R.; Bakare, G.N.; Adeshola, A.D.; Aliu, T. O.
    Green’s relations constitute five distinct equivalence classes that serve to define the elements of a semigroup. In this work, the equivalence classes within the Full Transformation Semigroup (Tκ) were systematically enumerated according to their respective heights, and the findings derived were subsequently generalized through the application of a combinatorial assertion and their graphical representations included to substantiate the theoretical results
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    On Nonexpansive and Expansive Semigroup of Order-Preserving Total Mappings in Waist Metric Spaces
    (Nigerian Society of Physical Sciences, 2022-12-22) Usamot, I. F.; Wahab, O. T.; Alata, S. M.; Tijani, K. R.
    In this paper, we introduce nonexpansive and expansive semigroup of order-preserving total mappings (ONTn) and (OETn), respectively, to prove some fixed point theorems in waist metric spaces. We examine the existence of mappings that satisfy the conditions ONTn and OETn. We also prove that every semigroup of order-preserving total mappings OTn has fixed point properties and that the set of fixed points is closed and convex. The present study generalised many previous results on semigroup of order-preserving total mappings OTn. E cacy of the results was justified with some practical examples.
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    Tropical Roots and Their Multiplicities on the Subsemigroup of Order-Decreasing and Order-Preserving Full Transformation
    (Lagos State University (LASU), 2024-12-12) Ibrahim, G. R.; Bakare, G. N.; Usamot, I. F.; Sulyman, O. I; Akinwunmi, S. A.; Adeshola, A.D.
    Let be ordered finite set. The tropical geometry was utilized to analyze the subsemigroup of order-decreasing and order-preserving semigroups, denoted as full transformation . The elements of classical algebra within were transformed into tropical polynomials, allowing for the determination of tropical roots and their multiplicities through the tropical curve, which was visualized using GeoGebra.