Browsing by Author "Mohammed, Ghazali Nasirudeen"

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    An efficient extragradient method for solving variational inequality problems with pseudo-monotone operators
    (Vertex Academic Press, 2026-01-20) Abdullahi, Muhammed Liman; Wahab, Olalekan Taofeek; Aderoju, Samuel Adewale; Mohammed, Ghazali Nasirudeen; John Dunama; Musa, Salaudeen Alaro
    Variational Inequality Problems (VIPs) provide a strong framework for exhibiting equilibrium problems in a variety of disciplines. Global Lipschitz continuity and strong monotonicity are two restrictive assumptions that are frequently used in traditional extragradient methods for solving VIPs, which limit their applicability to solve pseudo-monotone operators. This paper introduces a novel extragradient-type technique that eliminates the need for a global Lipschitz constant. A relaxation parameter that stabilizes the iterative process by taking a convex combination of the current point and a standard projection step is one of the two main innovations included in the new technique. The second innovation is an adaptive line search strategy that dynamically modifies the step size in response to local operator behaviour. We present a thorough convergence analysis that demonstrates the resulting sequence's weak convergence to a VIP solution. The suggested algorithm is more effective and reliable than previous approaches, especially for large-scale issues with sensitive initial circumstances, as shown by numerical experiments on well-known benchmark problems such as Sun's and Kojima-Shindo problems.
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    FIXED POINT THEOREMS OF CONDENSED KANNAN-TYPE CONTRACTION IN G-METRIC SPACES
    (2025-06-30) Wahab, Olalekan Taofeek; Musa, Salaudeen Alaro; Usman, Abdulazeez Adebayo; John, Dunama; Mohammed, Ghazali Nasirudeen
    In this paper, we introduce the notion of condensed Kannan-type contraction in G-metric spaces. We establish and prove some fixed point theorems of operators satisfying the condensed Kannan-type map. To evaluate the efficacy of this condition, we de fine a new criterion, called the alpha-measure, in G-metric spaces to seamlessly assess the effectiveness and dynamicity of the condensed map. We consider some practical examples to validate and demonstrate the dominance of the condensed map over some existing Kannan-type maps in G-metric spaces. The results obtained ensure suitability for solving unique and non-unique fixed points and suggest a framework for selecting an appropriate real constant alpha in (0; 1) for studying nonlinear operators.