Generalized Suzuki type  α-Z-contraction in b-metric space

The notions of a quasi-b-gauge space $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) and a left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family of generalized quasi-pseudo-b-distances generated by $(U,\textsl{Q}_{s ; \Omega })$ ( U , Q s ; Ω ) are introduced. Moreover, by using this left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -family, we define the left (right) $\mathcal{J}_{s ; \Omega }$ J s ; Ω -sequential completeness, and we initiate the Nadler type contractions for set-valued mappings $T:U\rightarrow Cl^{\mathcal{J}_{s ; \Omega }}(U)$ T : U → C l J s ; Ω ( U ) and the Banach type contractions for single-valued mappings $T: U \rightarrow U$ 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.

show abstract

“…The references [29][30][31][32][33][34][35][36][37][38][39] can be seen for other definitions and results in the setting of b-metric spaces.…”

Section: Definition 21 ([27]mentioning

confidence: 99%

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

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Also, Antal and Gairola 37 defined the generalized Suzuki type δ ‐Υ‐contraction with respect to ς in a b ‐metric space.…”

Section: Introductionmentioning

confidence: 99%

“…Definition (Antal and Gairola 37 ). Let

((), Q, m)

be a b ‐metric space with coefficient τ ≥ 1 and δ : Q × Q → R be a function.…”

Section: Introductionmentioning

confidence: 99%

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