Table of Content

Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications

Submission Deadline: 04 January 2023 Submit to Special Issue

Guest Editors

Prof. Hüseyin Işık, Bandırma Onyedi Eylül University, Turkey
Prof. Nawab Hussain, King Abdulaziz University, Saudi Arabia
Prof. Mujahid Abbas, Government College University, Pakistan
Prof. Naeem Saleem, University of Management and Technology, Pakistan

Summary

In a wide range of mathematical, computational, economical, modelling and engineering problems, the existence of a solution to a theoretical or real-world problem is equivalent to the existence of a fixed point for a suitable map. Fixed points are therefore of great importance in many areas of mathematics, sciences and engineering.

Fixed Point theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems.

Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed-point problems or optimization. Fixed point theory has several applications in theoretical and applied fields of mathematics, such as integral and differential equations and inclusions, dynamical system theory, mathematics of fractals, mathematical economics, and mathematical modelling. Fixed point procedures are a straightforward and efficient method for modelling, evaluating, and solving a wide range of data science problems.

The objective of this special issue is to report the latest advancements in the solutions of real-world problems, in particular by using the fixed/best-proximity point theory. We aim to provide a platform for researchers to promote, share, and discuss various new issues and developments in this area.The objective of this special issue is to report the latest advancements in the solutions of real-world problems, in particular by using the fixed/best-proximity point theory. We aim to provide a platform for researchers to promote, share, and discuss various new issues and developments in this area.

 

Fixed Point Theory in Banach space and Metric Spaces

Coincidence Point Theory and Applications

Application to Differential and Integral Equations

Fixed Point Theory in CAT(0) Spaces

Fixed Point Theory in Generalized Metric Spaces

Convergence and Stability Analysis of Iterative Methods

Applications of Fixed Point to Variational Inequality Problem, Split Feasibility Problem and Optimizations

Open Problems Related to Fixed Point Theory

Best Proximity Point Theory and Applications

Fixed Point and Approximate Fixed Point Theorems in Fuzzy Metric Spaces

Operator Inclusions in Function Spaces

Evolution Equations in Function Spaces

Stability of Functional Equations Related to Fixed Point Theory

Image/signal analysis

Optimal control problems

Machine learning/artificial intelligence


Keywords

Coincidence point; fixed point; vibrational inequality problem; best proximity points; evolution equations; operator inclusions; CAT (0) spaces; functions spaces; fuzzy metric spaces; image/signal analysis; machine learning; artificial intelligence

Published Papers


  • Open Access

    ARTICLE

    Quasi Controlled -Metric Spaces over -Algebras with an Application to Stochastic Integral Equations

    Ouafaa Bouftouh, Samir Kabbaj, Thabet Abdeljawad, Aziz Khan
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2649-2663, 2023, DOI:10.32604/cmes.2023.023496
    (This article belongs to this Special Issue: Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications)
    Abstract Generally, the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models. C*-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of research. The concept of a C*-algebra-valued metric space was introduced in 2014 to generalize the concept of metric space. In fact, It is a generalization by replacing the set of real numbers with a C*-algebra. After that, this line… More >

  • Open Access

    ARTICLE

    Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

    Nawab Hussain, Saud M. Alsulami, Hind Alamri
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2617-2648, 2023, DOI:10.32604/cmes.2023.023143
    (This article belongs to this Special Issue: Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications)
    Abstract In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results. More >

  • Open Access

    ARTICLE

    On Some Novel Fixed Point Results for Generalized -Contractions in -Metric-Like Spaces with Application

    Kastriot Zoto, Ilir Vardhami, Dušan Bajović, Zoran D. Mitrović, Stojan Radenović
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 673-686, 2023, DOI:10.32604/cmes.2022.022878
    (This article belongs to this Special Issue: Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications)
    Abstract The focus of our work is on the most recent results in fixed point theory related to contractive mappings. We describe variants of -contractions that expand, supplement and unify an important work widely discussed in the literature, based on existing classes of interpolative and -contractions. In particular, a large class of contractions in terms of and F for both linear and nonlinear contractions are defined in the framework of -metric-like spaces. The main result in our paper is that --weak contractions have a fixed point in -metric-like spaces if function F or the specified contraction is continuous. As an application… More >

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