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
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Open Access
ARTICLE
On Fractional Differential Inclusion for an Epidemic Model via L-Fuzzy Fixed Point Results
Maha Noorwali, Mohammed Shehu Shagari
CMES-Computer Modeling in Engineering & Sciences, DOI:10.32604/cmes.2023.028239
（This article belongs to this Special Issue:
Computational Aspects of Nonlinear Operator and Fixed Point Theory with Applications)
Abstract The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life
are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have
some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp
and deterministic; complete descriptions of real systems often require more comprehensive data than human
beings could recognize simultaneously, process and understand. Conventional mathematical tools which require
all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of practical situations.
Following the latter…
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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…
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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.
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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…
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