Some periodic and fixed point theorems on quasi-b-gauge spaces

N. Zikria; M. Samreen; T. Kamran; H. Aydi; C. Park

doi:10.1186/s13660-021-02750-4

Some periodic and fixed point theorems on quasi-b-gauge spaces

N. Zikria, M. Samreen, T. Kamran, H. Aydi^*, C. Park^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The notions of a quasi-b-gauge space (U, Q_s_;_Ω) and a left (right) J_s_;_Ω-family of generalized quasi-pseudo-b-distances generated by (U, Q_s_;_Ω) are introduced. Moreover, by using this left (right) J_s_;_Ω-family, we define the left (right) J_s_;_Ω-sequential completeness, and we initiate the Nadler type contractions for set-valued mappings T:U→ClJs;Ω(U) and the Banach type contractions for single-valued mappings T: U→ U, which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

Original language	English
Article number	13
Journal	Journal of Inequalities and Applications
Volume	2022
Issue number	1
DOIs	https://doi.org/10.1186/s13660-021-02750-4
Publication status	Published - 2022
Externally published	Yes

Keywords

Banach contraction
Fixed point
Generalized quasi-pseudo-b-distance
Nadler contraction
Periodic point
Quasi-b-gauge space

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10.1186/s13660-021-02750-4

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T1 - Some periodic and fixed point theorems on quasi-b-gauge spaces

AU - Zikria, N.

AU - Samreen, M.

AU - Kamran, T.

AU - Aydi, H.

AU - Park, C.

PY - 2022

Y1 - 2022

N2 - The notions of a quasi-b-gauge space (U, Qs;Ω) and a left (right) Js;Ω-family of generalized quasi-pseudo-b-distances generated by (U, Qs;Ω) are introduced. Moreover, by using this left (right) Js;Ω-family, we define the left (right) Js;Ω-sequential completeness, and we initiate the Nadler type contractions for set-valued mappings T:U→ClJs;Ω(U) and the Banach type contractions for single-valued mappings T: U→ U, which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

AB - The notions of a quasi-b-gauge space (U, Qs;Ω) and a left (right) Js;Ω-family of generalized quasi-pseudo-b-distances generated by (U, Qs;Ω) are introduced. Moreover, by using this left (right) Js;Ω-family, we define the left (right) Js;Ω-sequential completeness, and we initiate the Nadler type contractions for set-valued mappings T:U→ClJs;Ω(U) and the Banach type contractions for single-valued mappings T: U→ U, which are not necessarily continuous. Furthermore, we develop novel periodic and fixed point results for these mappings in the new setting, which generalize and improve the existing fixed point results in the literature. Examples validating our obtained results are also given.

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KW - Fixed point

KW - Generalized quasi-pseudo-b-distance

KW - Nadler contraction

KW - Periodic point

KW - Quasi-b-gauge space

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Some periodic and fixed point theorems on quasi-b-gauge spaces

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