Browsing by Author "Wangwe, Lucas"

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A CommonFixed Point Theorem for Generalised F-Kannan Mapping in Metric Space with Applications
(Hindawi, 2021) Wangwe, Lucas; Kumar, Santosh
This paper is aimed at proving a common fixed point theorem for F-Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. Wealso provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results
Common Fixed Point Theorems for Interpolative Rational-Type Mapping in Complex-Valued Metric Space.
(European Journal of Mathematics and Applications., 2024) Wangwe, Lucas
This paper aims to demonstrate the common fixed point theorem for interpolative rational-type contraction mapping in complex-valued metric spaces. Also provide an example for verification of the proven results. Further, as an application, the paper proves the existence and uniqueness solution of the R L C differential equation.
Existence of Maximal and Minimal Solutions Initial Value Problem for The System of Fractal Differential Equations
(Springer, 2025) Sajid,Mohammad; Kalita,Hemanta; Zengin, Gülizar Gülenay; Wangwe, Lucas
Differential equation refers to an equation that includes a function and its derivatives. These equations serve to model real-world situations where rates of change are significant. They are classified as either ordinary differential equations (ODEs) or partial differential equations (PDEs), depending on whether the unknown function is dependent on one or several independent variables, respectively. This paper presents a thorough investigation into fractal differential inequalities linked with an initial value fractal differential equation. It establishes the existence of a solution to this equation and demonstrates the convergence of both minimal and maximal solutions. Additionally, the paper introduces a comparative principle for evaluating solutions to the initial value problem associated with the fractal differential equation, ensuring a detailed and rigorous analysis of this subject.
Fixed point and common fixed point theorems for (ƴ S q)-F-Contraction mappings in b-Metric like spaces with Application.
(European Journal of Mathematics and Applications, 2023) Wangwe, Lucas
This paper proves some fixed point theorems for (ƴ s q )F- Kannan mappings and A common fixed point Theorem for (ƴ S q)-F- Reich type contraction mappings In a b-Metric Like space. Finally, We give an application to the solvability of a non linear integral equation.
Fixed point theorem on CATp(0) metric spaces with applications in solving matrix equations and fractional differential equations
(AIMS Mathematics, 2025-05-15) Sajid, Mohammad; Wangwe, Lucas; Hemanta, Kalita; Kumar, Santosh
This paper aimed to explore fixed point theorems for CMJ generalized mappings in CATp(0) metric spaces. To strengthen the established results, we presented a positive example. In applications, we found the existence of the solution to nonlinear matrix equations, and unique solutions of two scale fractal hybrid fractional differential equations in CATp(0).
Fixed point theorems for extended interpolative Kanann- iri¢-Reich-Rus non-self type mapping in hyperbolic complex-valued metric space
(Euro-Tbilisi Mathematical Journal, 2023) Wangwe, Lucas; Rathour, Laxmi; Mishra, Lakshmi N.; Mishra, Vishnu N.
This paper aims to demonstrate the xed point theorem for extended interpolative non-self type contraction mapping in hyperbolic complex-valued metric spaces. We provide an example for veri cation of the results. Further, as an application, we prove the existence and uniqueness of solutions for a class of Hadamard partial fractional integral equations by applying some fixed point theorems.
Fixed point theorems for generalized interpolative non expansive mappings in CATp(0) metric spaces
(2024-05-03) Wangwe, Lucas
This paper aims to prove xed point theorems for generalized interpolative non expansive mappings in CATp(0) metric spaces. Also provide a constructive example to support the proven results. The results proved here will be illustrated with an application to Hopf Bifurcations in a Delayed-Energy Based Model of Capital Accumulation.
Fixed point theorems for interpolative orthogonal relational in TVS-valued cone metric spaces
(Mbeya University of Science and Technology, Mbeya, 2025) Wangwe, Lucas
This article explores the fixed point theorem for a novel class of interpolative relation theoretical convex mappings in TVS-valued cone metric spaces, integrating relational theory, convexity, and interpolation properties to offer fresh perspectives and possible uses in theoretical and applied mathematics. An application of the results to differential equations and matrix equations in the context of orthogonal TVS-valued cone metric spaces is presented, along with a constructive example to support the findings.
Fixed Point Theorems for Rus-Hicks-Rhoades Contractive Mappings in Orthogonal Quasi-Metric Spaces With Applications to Orthogonal System Models
(Taylor & Francis, 2025-09-29) Wangwe, Lucas; Lupola, Ernesto; Mwangalika, Dickson
In this study, we explore fixed point theorems for Rus-Hicks-Rhoades-Jaggi hybrid combinational type mappings within orthogonal quasi-metric spaces. To illustrate and validate these results, an example is provided. Additionally, we highlight a practical application by connecting the theoretical findings to an orthogonal model in commu nication theory. Specifically, we relate the results to space-time block coding (STBC) in multiple-input multiple-output (MIMO) systems, where the fixed point solution repre sents the equilibrium state of iterative decoding, ensuring convergence to a stable codeword reconstruction even in the presence of channel disturbances. Moreover, we show that the Helmholtz equation with mixed boundary conditions possesses a unique f ixed point. This framework has broad applicability: in acoustics, it models vibrations in air columns of closed-open tubes; in electromagnetic, it describes field distributions in wave-guides and resonant cavities; and in mechanics, it represents vibrations of beams with one fixed and one free end. Such formulations demonstrate how Helmholtz phenomena under mixed boundary value problems provide insights into wave propa gation, resonance control, and system stability, thereby enriching both the theoretical understanding of fixed-point analysis and its engineering applications.
Investigation of some fixed point theorems for Various types of mappings in abstract spaces
(University of Dar es Salaam, 2022-03-01) Wangwe, Lucas
Fixed point theory is a fundamental tool in nonlinear functional analysis. It has many applications e.g. in Approximation theory, Optimisation theory, Variation inequalities, Game theory and Economics etc. The fixed point theory is a powerful tool to determine existence and uniqueness of the solutions of Differential equations, Integral equations, Partial differential equations, Fractional differential equations, Matrix equations and Functional equations. A fixed point problem can be stated as follows: Let X be a non-empty set and T : X !X be a mapping. A point x 2 X is a fixed point or invariant point of the mapping T if Tx = x. Does a fixed point exist for every map? Moreover, if such a point exists, is it unique, and how can we find it? We can distinguish three major approaches in fixed point theory: metric approach, topological approach, and discrete approach. Historically, these approaches were initiated by the discovery of major theorems: Brouwer fixed point theorem, Banach fixed point theorem, and Tarski fixed point theorem. In this thesis, we are concerned with the second approach, the metric fixed point theory. Fixed point theory and Banach contraction principle have been studied and generalised in different spaces, and various fixed-point theories were developed. Hence, this study investigated the fixed point theorems for various types of constructive mappings in various abstract spaces. The Banach contraction method has been used to obtain the fixed point theorems and their applications to ordinary and fractional differential equations. This study showed several ways to construct, extend, formulate, prove, and generalise fixed point theorems in abstract spaces using various maps, i.e., single valued maps, multivalued maps, hybrid maps and implicit maps. Also, the generalisation is done by considering relatively large classes of abstract spaces; Cone metric space, b-metric space, partial b-metric spaces, metric-like spaces, partial metric spaces, quasi partial Sb-metric-like spaces, and G-metric spaces. Finally, the proofs of the results are established by finding coincidence points or common fixed points.