Fixed Point Results for Generalized ℱ-Contractions in Modular b-Metric Spaces with Applications

Parvaneh, Vahid; Hussain, Nawab; Khorshidi, Maryam; Mlaiki, Nabil; Aydi, Hassen

doi:10.3390/math7100887

Cited by 16 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This section can be considered as an introduction to fundamental concepts of modular spaces and orthogonal modular spaces. For detailed information see [3,[21][22][23][24][25][26][27][28].…”

Section: Notations and Backgroundmentioning

confidence: 99%

Nadler’s Theorem on Incomplete Modular Space

et al. 2021

View full text Add to dashboard Cite

show abstract

Section: Notations and Backgroundmentioning

confidence: 99%

Nadler’s Theorem on Incomplete Modular Space

et al. 2021

View full text Add to dashboard Cite

show abstract

“…𝓁 , where 25 ) Let (Q, 𝜈) be a modular metric space and let k ≥ 1 be a real number. Take ℵ 𝓁 (𝜛, q) = (𝜈 𝓁 (𝜛, q)) k .…”

Section: Introductionmentioning

confidence: 99%

“…We also mention some basic topological terms as ℵ-convergent sequences, ℵ-Cauchy sequences, ℵ-complete spaces and ℵ-continuity of a function. Definition 4 (Parvaneh et al 25 ). Let (Q, ℵ) be a modular b-metric space.…”

Section: Introductionmentioning

confidence: 99%

“…(Ege and Alaca 24 ) Consider the space

l_{p} = \{(ϖ_{n}) \subset R : \sum_{n = 1}^{\infty} {|ϖ_{n}|}^{p} < \infty\} 0 < p < 1,

ℓ \in ((), 0, \infty)

and

ℵ_{ℓ} ((), ϖ, q) = \frac{d ((), ϖ, q)}{ℓ}

, where

d (ϖ, q) = {(\sum_{k = 1}^{\infty} {|ϖ_{k} - q_{k}|}^{p})}^{\frac{1}{p}}, ϖ = ϖ_{k}, q = q_{k} \in l_{p}

It could be easily seen that

((), Q, ℵ)

is a modular b ‐metric space. Example 2. (Parvaneh et al 25 ) Let

((), Q, ν)

be a modular metric space and let k ≥ 1 be a real number. Take

ℵ_{ℓ} ((), ϖ, q) = {((), ν_{ℓ} ((), ϖ, q))}^{k}

.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fixed point results for Suzuki‐type Σ‐contractions via simulation functions in modular b‐metric spaces

Öztürk

Büyükkaya

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

This study aims to introduce Suzuki-type Σ-contraction mappings with simulation functions in the framework of modular b-metric spaces. Some coincidence and common fixed point results are obtained for four mappings with the weak compatibility property. Outcomes are the extensions and improvements of the existing literature. Finally, we also present two applications on graph theory and homotopy theory, which show the applicability and validity of our results.

show abstract

“…Kılınç and Alaca [12] proved that two main fixed point theorems for commuting mappings in modular metric spaces. Recently, many authors [13,14,15,16,17,18,19,20,21,22,23,24,25,26], studied on different fixed point results for modular metric spaces. In 2014 Khamsi and Abdou investigated Hausdorff metric modular in modular metric spaces [27], and proved fixed point theorem for multi-valued mappings.…”

Section: Introductionmentioning

confidence: 99%