Some New Observations on Geraghty and Ćirić Type Results in b-Metric Spaces

Mlaiki, Nabil; Dedović, Nebojša; Aydi, Hassen; Gardašević-Filipović, Milanka; Bin‐Mohsin, Bandar; Radenović, Stojan

doi:10.3390/math7070643

Cited by 15 publications

(11 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several authors generalise the previous theorem in various directions [2,5,7,9,10,11,12,13,14,17,15].…”

Section: Thenmentioning

confidence: 99%

Fixed point theorems in controlled rectangular metric spaces

Rossafi¹,

Kari²

2022

Preprint

View full text Add to dashboard Cite

In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality as follows:for all distinct x, y, u, v ∈ X with the function α : X × X → [1, ∞[. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.

show abstract

“…Several authors generalise the previous theorem in various directions [2,5,7,9,10,11,12,13,14,17,15].…”

Section: Thenmentioning

confidence: 99%

Fixed point theorems in controlled rectangular metric spaces

Rossafi¹,

Kari²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Various fixed point results were established on such spaces. For more information on b-metric spaces and b-metric-like spaces, the readers can refer to (see [6][7][8][9][10][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

New fixed point theorems for θ - ϕ -contraction on b -metric spaces

Rossafi¹,

Kari²,

Park³

et al. 2022

J. Math. Computer Sci.

View full text Add to dashboard Cite

In this paper, we define θ-φ-contraction on a b-metric space into itself by extending θ-φ-contraction introduced by Zheng et al. [D. W. Zheng, Z. Y. Cai, P. Wang, J. Nonlinear Sci. Appl., 10 (2017), 2662-2670] in metric space and also, we prove θ-type theorem in the setting of b-metric spaces as well as θ-φ-type theorem in the framework of b-rectangular metric spaces. Moreover, we give some applications to nonlinear integral equations. We also give illustrative examples to exhibit the utility of our results.

show abstract

“…Many authors proved fixed point theorems for quasi-contraction mappings in b-metric spaces with some more restriction on values of q (see, for example, [20,[22][23][24][25]). More on b-metric spaces can be found in [26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

Jain

Kaur

2021

Axioms

View full text Add to dashboard Cite

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

show abstract

Some New Observations on Geraghty and Ćirić Type Results in b-Metric Spaces

Abstract: We discuss recent fixed point results in b-metric spaces given by Pant and Panicker (2016). Our results are with shorter proofs. In addition, for ε ∈ ( 1 , 3 ] , our results are genuine generalizations of ones from Pant and Panicker.

Cited by 15 publications

References 30 publications

Fixed point theorems in controlled rectangular metric spaces

Fixed point theorems in controlled rectangular metric spaces

New fixed point theorems for θ - ϕ -contraction on b -metric spaces

Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

Contact Info

Product

Resources

About