These metric spaces lie within the modular space context since the above distances can be written as rho x-y where rho is a modular see 23 27 30 for detailed information on the subjectFixed point theory for modular spaces has been mostly developed for convex modulars 12 13. Some properties are also discussed with examples.
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Some properties are also discussed with examples.
Modular g metric spaces. Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. Modular metric spaces were introduced in 2 3. Also we prove a fixed point theorem for mappings satisfying sufficient conditions in soft G-metric spaces.
Classification of space-like translation surfaces in the 3-dimensional Lorentz Heisenberg group H3 Rafik Medjati Hanifi Zoubir Brahim Medjahdi. Their approach was fundamentally different from the one studied in 2 3. 7 rows This article introduces a new type of C-algebra valued modular G-metric spaces that is more.
A modular G-metric space X_omegaG is said to be modular G-complete if every modular G-Cauchy sequence in X_omegaG is modular G-convergent in X_omegaG. ωλx xo 0as λ and X ω X ωxo x X. This article introduces a new type of C-algebra valued modular G-metric spaces that is more general than both C-algebra valued modular metric spaces and modular G-metric spaces.
A few common fixed. There were any authors introduced the generalization of metric spaces such as Gahler 4 which called 2metric spaces and Dhage 3 which called Dmetric spaces. We introduce the notion of α-type F-contraction in the setting of modular metric spaces which is independent from one given in Hussain et al.
4 νλxyzνλ 2 xazνλ 2 ayz for all λ0. Motivated by Gopal et al. A few common fixed point results in C-algebra valued modular G-metric spaces are discussed using the C-class function along with some suitable examples to.
The obtained results encompass various generalizations. A modular G-metric space X ω G is said to be modular G-complete if every modular G-Cauchy sequence in X ω G is modular G-convergent in X ω G. These are related to contracting generalized average velocities rather than metric distances and the successive approximations of fixed points converge to the fixed points in the modular sense which is weaker than the metric convergence.
Then we obtain soft convergence and soft continuity by using soft G-metric. Where Xω and X ω are said to be modular spaces. Theorem 31 Let X ω G be a G-complete non-symmetric modular G-metric space satis- fyin g a 3 -type condition such that C 2 C 4 0 1 4 ρ and let T.
Let X ω G be a modular G-metric space then x n n N X ω G is said to be modular G-Cauchy if for every ϵ 0 there exists n ϵ N such that ω λ G x n x m x l ϵ for all n m l n ϵ and λ 0. Modular function spaces are a special case of the theory of modular vector spaces introduced by Nakano 13. 1 If νλxyz0 for all λ0 then x yz.
On the modular G-metric spaces and fixed point theorems. If is a convex modular on according to 1 2 the two modular spaces coincide that is and this common set can be endowed with the metric given by for any. Some properties are also discussed with examples.
Integral type contractions in modular metric spaces. We introduce the notion of modular Gmetric spaces and obtain some fixed point theorems of contractive mappings defined on modular Gmetric spaces. In Fixed Point Theory Appl.
Journal of Inequalities and Applications 2013 1 1-14 2013. Metric modular spaces I basic concepts. It follows from 1 2 that if is a modular on then the modular space can be equipped with a nontrivial metric generated by and given by for any.
This article introduces a new type of C-algebra valued modular G-metric spaces that is more general than both C-algebra valued modular metric spaces and modular G-metric spaces. 100 of your contribution will fund improvements and new initiatives to benefit arXivs global scientific community. ωλ νx y ωλx z ωνz y for λ ν 0.
Chistyakov 69 rectified in absorbing manner the structure of a metric modular space and introduced a first countable and Hausdorff topology on it which is very popular in contemporary research these daysNow we study the concept of the Hausdorff distance of a given generalized metric modular space on nonempty compact subsets. Fix xo X. The notion of a modular metric on an arbitrary set an the corresponding modular space more general than a metric space were introduced and studied recently by Chistyakof 1.
A few common fixed point results in C-algebra valued modular G-metric spaces are discussed using the C-class function along with some. The notion of modular spaces as a generalization of metric spaces was introduced by Nakano and was intensively developed by Koshi Shimogaki Yamamuro 19 26 34 and othersThe complete development of these theories is due to Luxemburg Mazur Musielak Orlicz Turpin 24 25 27 33 and their collaboratorsModular metric space was introduced in 6 7. Fixed point theory in modular metric spaces was studied by Abdou and Khamsi 1.
Further Jungck 3 introduced more generalized commutativity the so-called compatibility which is more general than weak commutativity. The purpose of this paper which is split into two parts is to define the notion of a modular on an arbitrary set develop the theory of metric spaces generated by modulars called modular metric spaces and on the basis of it define new metric spaces of multivalued functions of bounded generalized variation of a real variable with values in metric semigroups and abstract convex cones. B Azadifa M Maramaei G Sadeghi.
Our general framework will be the modular function space setting. Further we establish some fixed point and periodic point results for such contraction. ωλx xo forλ 0.
Definition 26 Let g and h be single-valued self-mappings on a set X. 3 νλxyy2νλ 2 xxy for all λ0. Let X ω be a modular metric space.
We introduce soft G-metric spaces via soft element. As an application we use the concept of contraction and the. 2 νλxyzνλ 2 xxyνλ 2 xxz for all λ0.
X ω G X ω G be a mapping. CiteSeerX - Document Details Isaac Councill Lee Giles Pradeep Teregowda. Set Xω Xωxo x X.
In the Lorentz Heisenberg space H3 endowed with flat metric g3 a translation surface is parametrized by rx y γ 1 xγ 2 y where γ. In this chapter we present yet one more application of the metric modulars theory to the existence of fixed points of modular contractive maps in modular metric spaces. Let Xν be a modular G-metric space induced by metric modular ν for any xyza Xν it follows that.
B Azadifar G Sadeghi R Saadati C Park. Let X d be a metric space the self-mappings f g are said to be weakly commuting if d f g x g f x d g x f x for all x X.
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