Browsing by Author "Musa, Salaudeen Alaro"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    Condensed Kannan-Type Maps and Their Efficiency Measures in Complete Metric Spaces
    (2025-09-25) Wahab, Olalekan Taofeek; Ibrahim-Garba, Risqot; Musa, Salaudeen Alaro
    Recently, some studies introduced interpolative Kannan-type maps for solving non-unique fixed-point problems. However, these studies do not offer a technique for determining the fractional powers of the maps, which would be useful in approximating the fixed points. This study uses two symmetry terms of the conventional Kannan contraction to define a novel condensed Kannan-type contraction in complete metric spaces. By imposing the condensed map on the Picard operator, we prove the existence of unique and non-unique fixed points. We also define a criterion for selecting an appropriate real constant α suitable for approximating the fixed points of the condensed map. We consider two practical and numerical examples to show both the versatility and validity of the hypotheses of this study. These results show that the class of condensed maps is strictly larger than the existing class Kannan-type maps, ensure suitability for solving both unique and non-unique fixed points, and do so with a better convergence rate.
  • Thumbnail Image
    Item
    Constructive approach and randomization of a two-parameter chaos system for securing data
    (FLAYOO Publishing House Limited, 2024-05-21) Wahab, Olalekan Taofeek; Musa, Salaudeen Alaro; Jimoh, Abdulazeez Kayode; Dauda, Kazeem Adesina
    Secure communication techniques are important due to the increase in the number of technology users across the world. Likewise, a more random encryption algorithm suitable to secure data from unauthorised users is highly expected. This paper proposes a two-parameter nonlinear chaos map that is sensitive to the trio seed (s0, \alpha, \lambda) and has better information encryption. We introduce the parameter \alpha to linearise the conventional chaos system, which in turn brings a delay in the cryptosystems. The delay is a phenomenon that changes the chaotic features of a system. A small delay in the system leads to more aperiodicity and the unpredictability of the chaotic attractions. We normalise the new chaos map and use the Lipschitz and pseudo-contractive operators to obtain its irregularity region in Hilbert spaces. We also analyse the chaos map in terms of trajectory, Lyapunov exponent, complexity, and information entropy. Results obtained show that the new chaos map has a wide chaotic range and better statistical properties. It also maintains low complexity due to its linearity and produces more key spaces than most existing chaotic maps.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    On enriched weakly contractive map in Hilbert spaces
    (International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2025-10-11) Wahab, Olalekan Taofeek; Musa, Salaudeen Alaro; Usman, Abdulazeez Adebayo
    This paper introduces a class of enriched weakly contractive mappings for approximating a non-Picard average operator on a closed convex subset of Hilbert spaces. By imposing the enriched weakly mapping on the average operator, we establish and prove some results concerning convergence theorems (strong and weak), stability, and convergent rate. The validity and gen erality of the new class of enriched weakly mappings are examined with the aid of practical examples. The results harmonize and improve some recent results on enriched contractive-type mappings.
  • Thumbnail Image
    Item
    Results on condensed Kannan-type 2-cyclic map in b-metric spaces
    (SCIK Publishing Corporation, 2026-03-30) Musa, Salaudeen Alaro; Wahab, Olalekan Taofeek; Aliu, Tajudeen Olaniyi; Fatai, Musa Olajide; Anise, Musiliudeen Adisa
    Some authors recently proposed a condensed Kannan-type map that can solve nonlinear problems with unique and non-unique solutions. However, these findings may not address all situations involving inexact spaces. This study presents a strategy for proving fixed points of Kannan-type 2-cyclic contractions by condensation in inexact spaces, commonly referred to as b-metric spaces. We further extend the findings to study fixed points of trivially cyclic mappings. With the aid of examples comprising cyclic and trivially cyclic mappings, we validate all hypotheses of this study. The results show that the condensed cyclic Kannan-type map is more elaborate than the previous Kannan-type cyclic maps in the literature, solves problems with the inexact structures, and ensures unique and non-unique fixed points.