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Talk 01 — Mantu Saha (The University of Burdwan, India) — [computing…]Local time: click here to view in your time zoneTitle: A study on some class of generalized enriched F-contractions and their applications
Abstract
This talk introduces various classes of possibly non-continuous contractive mappings, termed as generalized enriched F-contractions. Numerous fixed point and common fixed point theorems for these classes have been proved, supported with several non-trivial examples, illustrating that these mapping may be discontinuous at the fixed point. Furthermore, the applicability of these findings have been demonstrated to solve the Volterra type integral equations and related systems, exhibiting the theoretical significance and practical relevance of these nonlinear mappings.
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Talk 02 — Anita Tomar (Pt. L. M.S.Campus, Sridev Suman Uttarakhand University, Rishikesh, India) — [computing…]Local time: click here to view in your time zoneTitle: Fixed Point Theory and Applications: New Directions in Metric Spaces and Nonlinear Analysis
Abstract
This talk explores recent generalizations in fixed point theory and its applications, with a particular focus on developments in metric spaces. We investigate extensions of fixed circles in diverse settings, providing new perspectives on fixed geometric structures and self-mappings with multiple fixed points. These contributions aim to enrich the theoretical framework of fixed point theory while addressing complex nonlinear phenomena. Furthermore, the practical relevance of these advancements is examined in areas such as neural networks and artificial intelligence, where fixed point techniques play a significant role in modeling and convergence analysis. The work also highlights the integration of fixed point methods with contemporary mathematical structures, including fractal systems and iterative dynamics. Emerging research directions, open problems, and interdisciplinary opportunities are discussed, emphasizing the continued importance of fixed point theory in modern mathematical and applied research. By bridging theoretical insights with practical implementation, this study demonstrates how fixed point theory serves as a unifying and powerful tool for solving nonlinear problems across diverse scientific domains.
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Talk 03 — Dagnachew Jenber Negash (Addis Ababa Science and Technology University, Ethiopia) — [computing…]Local time: click here to view in your time zoneTitle: An inertial method for the solution of M-tuple split common fixed point problems involving strict quasi-G_f-pseudocontractive mappings
Abstract
This work presents an inertial method to estimate solutions to the m-tuple split common fixed point problems for strict quasi-G_f-pseudocontractive mappings in (m+1) Banach spaces. Our approach can also be used to solve the extended split equality fixed point problem. Applications to the solution of extended split equality issues, such as Extended Split Equality Equilibrium Problem, Extended Split Equality Inclusion Problem, Minimization of Tikhonov Functionals in Banach Spaces and Extended Split Equality Feasibility Problem are demonstrated in the setting of real Banach spaces. To illustrate our conclusions, we end with a numerical example.
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Talk 04 — Solomon Bekele Zegeye (Debre Berhan University, Department of Mathematics, Ethiopia) — [computing…]Local time: click here to view in your time zoneTitle: APPROXIMATION OF COMMON SOLUTIONS OF NONLINEAR PROBLEMS IN BANACH SPACES
Abstract
Fixed point theory, as an important branch of nonlinear analysis theory, has played very important roles in many different fields. The topic of approximation of fixed points of mappings is as useful as existence theorems for applied mathematics. Approximation methods can also be applied to prove the solvability of optimization problems, differential equations, variational inequalities and equilibrium problems. In this talk, we propose an algorithm for solving a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of $f$-fixed points of a finite family of $f$-pseudo-contractive mappings and the set of solutions of a finite family of variational inequality problems for Lipschitz monotone mappings in real reflexive Banach spaces. In addition, we give numerical results to demonstrate the applicability and efficiency of the proposed method.
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Talk 05 — Mujahid Abbas (University of Johannesburg, South Africa) — [computing…]Local time: click here to view in your time zoneTitle: Fixed points of multivalued friendly mappings
Abstract
The aim of this talk is to introduce the notion of friendly mappings using commutative diagram. The concept is illustrated with the help of some examples. It is shown that if the set of fixed point of a mapping is nonempty, then the set of fixed points of a friendly mapping is also nonempty. The concept of multivalued friendly mapping is also defined. The necessary conditions for the existence of fixed points of multivalued friendly mappings are studied.
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Talk 06 — Mengistu Goa Sangago (University of Botswana, Botswana) — [computing…]Local time: click here to view in your time zoneTitle: Fixed point approach to constrained convex minimization problems and equilibrium problems
Abstract
In this presentation, we discuss fixed point approach to a constrained convex minimization problem and a generalized equilibrium problem. We also explore some iterative schemes in approximating a common solution of a constrained convex minimization problem, an equilibrium problem and a fixed point problem of a nonlinear mapping in the literature. Finally, we review the iterative schemes in the literature compared to the well known gradient projection algorithm (GPA).
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Talk 07 — Hagos Hailu Gidey (Botswana International University of Science and Technology, Botswana) — [computing…]Local time: click here to view in your time zoneTitle: SOLVING SPLIT MULTI-VARIATIONAL INEQUALITY PROBLEMS IN BANACH SPACES
Abstract
In this paper, we introduce the multi-valued split equality Minty variational inequality problem and develop an inertial algorithm to solve it in Banach spaces. We establish a strong convergence result under the assumptions that one of the mappings involved is a uniformly continuous multi-valued quasi-monotone mapping, while the other is a multi-valued quasi-Bregman strictly pseudocontractive mapping. Additionally, we present specific applications of the main result and conclude with a numerical example to demonstrate the effectiveness of our method.
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Talk 08 — Abebe Regassa Tufa (University of Botswana, Botswana) — [computing…]Local time: click here to view in your time zoneTitle: Iterative Methods for Finding Fixed Points of Enriched Non-self Mappings in Hilbert Spaces
Abstract
This study develops and analyzes iterative algorithms for approximating fixed points of enriched strict pseudocontractive non-self mappings in Hilbert spaces, a class that properly generalizes enriched strict pseudocontractive mappings. In addition, we investigate iterative schemes for enriched quasi-nonexpansive non-self mappings, which extend the corresponding enriched quasi-nonexpansive framework. Under suitable conditions, we establish both weak and strong convergence results for the proposed methods. The obtained results unify, extend, and improve several existing findings in the literature.
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Talk 09 — Elvin Rada (University of Elbasan "Aleksander Xhuvani", Albania) — [computing…]Local time: click here to view in your time zoneTitle: INERTIAL-TYPE ALGORITHMS FOR MULTIVALUED1 JAGGI-TYPE F -CONTRACTIONS IN BANACH SPACES WITH APPLICATION
Abstract
In this paper, we present a mathematically consistent version of the inertial approach for multivalued contractive mappings. Since inertial iterations require linear operations, we work in a real Banach space. We introduce a multivalued Jaggi-type F -contractive condition formulated by means of the Hausdorff metric and prove the existence of fixed points for multivalued mappings with closed graphs. Under an additional endpoint contractive assumption, we establish the uniqueness of the endpoint, the strong convergence of an inertial Krasnosel’skiı–Mann type algorithm with summable errors, and Ulam–Hyers stability in endpoint form. Finally, we apply the abstract results to a class of nonlinear integral inclusions arising from a second-order differential inclusion with Dirichlet boundary conditions.
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Talk 10 — Maria Amarakristi Onyido (Northern Illinois University, USA) — [computing…]Local time: click here to view in your time zoneTitle: On the Weak Solutions of Elliptic Equations with Nonlinear Boundary Conditions
Abstract
Recent studies have considered elliptic equations with nonlinear boundary conditions, establishing the existence and multiplicity of solutions through several techniques, including fixed point theory. This talk will present some of our studies and results in this direction, with a focus on equations with nonlinearities both on the interior and on the boundary. Analysis of such equations often requires addressing some eigenvalue equations for the linearization at an equilibrium solution. Hence, we shall address the principal spectral theory of a coupled Steklov-Robin eigenvalue problem and its applications.
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Talk 11 — Markjoe O. Uba (Northern Illinois University, USA) — [computing…]Local time: click here to view in your time zoneTitle: Computing fixed points of generalized non-expansive-type maps and mixed equilibrium problems
Abstract
Let $\Omega$ be a nonempty, closed, and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. This talk discusses an algorithm for finding a common element of the set of solutions to a generalized mixed equilibrium problem and the set of common fixed points of a family of a general class of nonlinear nonexpansive maps. The results obtained are then applied to the study of an optimization problem.
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Talk 12 — Yirga Abebe Belay (Naresuan University, Thailand) — [computing…]Local time: click here to view in your time zoneTitle: Solutions of Perturbed Krasnoselskii-Mann iterations and their applications to image restoration problems
Abstract
This paper introduces an inertial method for solving the general perturbed Krasnoselskii-Mann type algorithm in Hilbert space settings, where the underlying mapping is quasi-nonexpansive. The convergence property of the method has been analyzed under some mild assumptions on the control parameters. A numerical example has been provided to demonstrate the effectiveness of the method and to compare its convergence performance against the results in the literature. Finally, the proposed method was employed in solving image restoration problems. For the application, the standard optimization problem for image restoration has been transformed into its equivalent monotone inclusion problem. Then the monotone inclusion problem has been changed into the fixed point problem. We evaluate the quality of the improvement in the Signal-to-Noise Ratio (ISNR) and the restored images using the Structural Similarity Index Measure (SSIM) metrics. The quality of images restored by the proposed method has also been compared to those restored by the existing methods using the ISNR and SSIM metrics.
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Talk 13 — Umesh Chandra Gairola (H.N.B.Garhwal University, India) — [computing…]Local time: click here to view in your time zoneTitle: Some fixed point results on finite product of metric spaces
Abstract
With a view to generalize the Banach contraction principle, Professor Januj. Matkowski announces a result for a system of n transformations on the finite product of metric spaces in Police Academy of Sciences 1971, which is known as Matkowski's Contraction Principle(MCP).Matkowski result is applicable to find the solution of a system of functional equations, which attracts several mathematicians to work along this direction. In this talk, we will discuss some extensions and development of MCP.
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Talk 14 — Anarul Islam Mondal (National Institute of Technology Rourkela, India) — [computing…]Local time: click here to view in your time zoneTitle: Fixed Point Theorems for Generalized Rakotch Contractions in Equivalent-Distance Spaces
Abstract
E-Rakotch contractions are introduced in the setting of equivalent-distance spaces, where variable contractive behavior is combined with controlled geometric distortion. A fixed point theorem is established ensuring existence, uniqueness, and convergence of Picard iteration in complete metric spaces. Classical Banach and Rakotch principles are recovered as special cases. An illustrative example and an application to a nonlinear algebraic equation are presented.