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Metric Modular Spaces

, 2015
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces.
Chistyakov, Vyacheslav
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C*-Algebra-Valued Partial Modular Metric Spaces and Some Fixed Point Results

Symmetry, 2023
In the present paper, we introduce the notion of C*-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, C*-algebra-valued partial metric space, and C*-algebra-valued modular metric ...
Salvatore Sessa, Dipankar Das, Yumnam Mahendra Singh   +2 more
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Modular Metric Spaces

2015
The concept of a metric space is closely related to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of metric is a generalization of the Euclidean metric arising from the basic long known properties of the Euclidean distance.
Mohamed A. Khamsi, Wojciech M. Kozlowski
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Existence Theory on Modular Metric Spaces

2018
Since the year 1922, Banach’s contraction principle, due to its simplicity and usability, has become a popular tool in modern analytics, particularly in nonlinear analysis, including the use of equations, differential equations, variance, equilibrium problems, and much more (see, e.g., [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]).
Anantachai Padcharoen, Parin Chaipunya, Poom Kumam   +2 more
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Fixed point results in orthogonal modular metric spaces

2020
Summary: First we generalize the notion of \(O\)-sets and then we establish some fixed point theorems for Banach's contraction and Suzuki type \(\Theta\)-contraction in the setting of orthogonal modular metric spaces. The obtained results extend, generalize and improve many fixed point results given by some authors in the literature.
Hosseini, Hoda, Eshaghi Gordji, Madjid
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Modular metric spaces, I: Basic concepts

Nonlinear Analysis: Theory, Methods & Applications, 2010
The author introduces the notion of a (metric) modular as follows: A (metric) modular on a set \(X\) is a function \(w:(0,\infty)\times X\times X\rightarrow [0,\infty]\) satisfying, for all \(x,y,z\in X,\) the following three properties: \(x=y\) if and only if \(w(\lambda,x,y)=0\) for all \(\lambda >0;\) \(w(\lambda,x,y)=w(\lambda,y,x)\) for all ...
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Meir–Keeler type contractive mappings in modular and partial modular metric spaces

Asian-European Journal of Mathematics, 2019
In this paper, first, we introduce the class of [Formula: see text]-Meir–Keeler contractive mappings and establish some fixed point results. Next, we introduce the notion of partial modular metric space and establish some fixed point results in this new spaces.
Hasan Hosseinzadeh, Vahid Parvaneh
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Modular A-Metric Spaces

2020
AYDIN, Elif/0000-0002-7620 ...
Aydin, Elif, Kutukcu, Servet
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Some results for cyclic weak contractions in modular metric space

2023
Summary: In this paper, we present some fixed point results for cyclic weak \(\phi\)-contractions in \(\omega\)-complete modular metric spaces and \(\omega\)-compact modular metric spaces, respectively. Some results for contractions that have zero cyclic properties are also provided.
Rahimpoor, Hossein, Nikoufar, Ismail
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Modular metric spaces, II: Application to superposition operators

Nonlinear Analysis: Theory, Methods & Applications, 2010
The author presents an exhausting description of Lipschitz continuous and some other classes of nonlinear superposition operators acting in modular metric spaces of functions of a real variable of finite generalized variation in the sense of \textit{M. Schramm} [Trans. Am. Math. Soc.
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