A new generalization of metric spaces: rectangular M-metric spaces

Özgür, Nihal Yılmaz; Mlaiki, Nabil; Taş, Ni̇hal; Souayah, Nizar

doi:10.1007/s40096-018-0262-4

Cited by 23 publications

(32 citation statements)

References 8 publications

(8 reference statements)

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“…Hence, all the requirements of Theorem 2 are fulfilled and ς = 1 is a unique fixed point of f . The following corollary deduced form Theorem 2, which remains genuinely sharpened version of Theorem 4.2 of Özgür et al [16]. for all ς, σ ∈ χ, we have…”

Section: Remarkmentioning

confidence: 66%

“…In 2016, Mlaiki et al [15] introduced the notion of an M b -metric spaces and utilized the same to prove fixed point results. Later on, in an attempt to extend the classes of "rectangular metric spaces" and "M-metric spaces", Özgür [16] introduced the class of rectangular M-metric spaces. On the other hand, in 2018, Mlaiki et al [17] generalized the class of M b -metric spaces by introducing the the…”

Section: Introductionmentioning

confidence: 99%

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Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

et al. 2019

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In this paper, we enlarge the classes of rectangular M b -metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular M rξ -metric spaces and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of solution for a system of Fredholm integral equation. Mathematics 2019, 7, 1136 2 of 15 class extended M b -metric spaces. Very recently, Asim et al. [18] introduced the class of rectangular M b -metric space and utilized the same to prove an analogue of Banach contraction principle. Soon, Asim et al. [19] generalized the class of rectangular M b -metric spaces by introducing the class of M ν -metric spaces.Inspired by foregoing observations, we introduce the class of extended rectangular M rξ -metric spaces and utilize the same to prove fixed point result in such spaces. We, also furnish an example to establish the genuineness of our newly proved result. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation. Definition 6.[12] Let χ = ∅ and ξ : χ × χ → [1, ∞). A mapping r ξ : χ × χ → R + is said to be an extended rectangular b-metric on χ if, r ξ satisfies the following (for all ς, σ ∈ χ and all distinct ρ, ∈ χ \ {ς, σ}):

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Section: Remarkmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

et al. 2019

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“…In 2014, Asadi et al [5] introduced the notion of an M-metric spaces as follows: In 2018, Özgür [25] introduced the notion of rectangular M r -metric spaces as follows:…”

Section: Notation 1 ([5])mentioning

confidence: 99%

“…However, many researchers generalized and extended the Banach contraction principle in numerous ways by improving contraction conditions, using auxiliary mappings, and enlarging the class of metric spaces for this kind of results. One may recall the existing notions, namely of partial metric space [16], partial symmetric space [9], partial JS-metric space [7], metric like space [1], b-metric space [14], rectangular metric space [8,12], cone metric space [15], M-metric space [5], M b -metric space [18], rectangular M-metric space [25], and several others. Very recently, Asim et al [10] introduced the class of rectangular M rb -metric spaces to enlarge the classes of M b -metric spaces and rectangular M-metric spaces wherein the newly refined ideas are utilized to prove some fixed point results.…”

Section: Introductionmentioning

confidence: 99%

“…In 2014, Asadi et al [5] extended the partial metric spaces (see [17]) by introducing Mmetric spaces and utilized the same to prove fixed point results, which were extended in many ways (see [2-4, 6, 13, 19-27]). Thereafter, Özgür [25] extended both the rectangular metric spaces and M-metric spaces by introducing rectangular M r -metric spaces which were used to prove fixed point results.…”

Section: Introductionmentioning

confidence: 99%

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Fixed point results in $M_{\nu }$-metric spaces with an application

2019

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In this paper, we introduce the concept of M ν-metric as a generalization of M-metric and ν-generalized metric and also prove an analogue of Banach contraction principle in an M ν-metric space. Also, we adopt an example to highlight the utility of our main result which extends and improves the corresponding relevant results of the existing literature. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation.

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On fixed point and its application to the spread of infectious diseases model in M_v^b‐metric space

Alam,

Rohen,

Tomar

2024

Math Methods in App Sciences

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This work aims to prove new results in an ‐metric space for a noncontinuous single‐valued self‐map. As a result, we extend, generalize, and unify various fixed‐point conclusions for a single‐valued map and come up with examples to exhibit the theoretical conclusions. Further, we solve a mathematical model of the spread of specific infectious diseases as an application of one of the conclusions. In the sequel, we explain the significance of ‐metric space because the underlying map is not necessarily continuous even at a fixed point in ‐metric space thereby adding a new answer to the question concerning continuity at a fixed point posed by Rhoades. Consequently, we may conclude that the results via ‐metric are very inspiring, and underlying contraction via ‐metric does not compel the single‐valued self‐map to be continuous even at the fixed point. Our research is greatly inspired by the exciting possibilities of using noncontinuous maps to solve real‐world nonlinear problems.

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A new generalization of metric spaces: rectangular M-metric spaces

Cited by 23 publications

References 8 publications

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

Fixed point results in $M_{\nu }$-metric spaces with an application

On fixed point and its application to the spread of infectious diseases model in M_v^b‐metric space

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A new generalization of metric spaces: rectangular M-metric spaces

Cited by 23 publications

References 8 publications

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

Extended Rectangular Mrξ-Metric Spaces and Fixed Point Results

Fixed point results in $M_{\nu }$-metric spaces with an application

On fixed point and its application to the spread of infectious diseases model in Mvb‐metric space

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On fixed point and its application to the spread of infectious diseases model in M_v^b‐metric space