On the Conditions of Fixed-Point Theorems Concerning 
                
                  
                
                $$\varvec{F}$$
                
                  
                    
                      F
                    
                  
                
              -Contractions

Kajántó, Sándor; Lukács, Andor

doi:10.1007/s00025-018-0846-1

Cited by 4 publications

(6 citation statements)

References 7 publications

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“…Since κh 4 − κh 2 + 1 ≤ 1 s 2 , from Lemma (6) with ℵ = 1, we conclude that {ν p } = {T p ν 0 } is a Cauchy sequence. With the completeness of (Z, b), {ν p } converges to some point ν * ∈ Z; that is, we have…”

Section: Fixed-point Theoremsmentioning

confidence: 72%

“…Recently, other authors demonstrated (in various methods) Wardowski's original results in the absence of both requirements (F 2 ) and (F 3 ) (see [6,7]). For more on this direction, consult [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 96%

“…Lukács and Kajántá [6] refined Wardowski's theorem in the context of b-MS and dropped condition (F 2 ). Following that, several authors demonstrated (through various methods) Wardowski's original results in the absence of both conditions (F 2 ) and (F 3 ) (see [7,36]).…”

Section: Introductionmentioning

confidence: 99%

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Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

et al. 2023

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The purpose of this paper is to define the notion of extended convex F contraction by imposing less conditions on the function F satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory.

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Section: Fixed-point Theoremsmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 96%

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Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

et al. 2023

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“…Later, Wardowski [5], using λ as a function, demonstrated a fixed-point theorem for -contractions. Recently, some authors demonstrated the Wardowski original conclusions without the criteria ( 2 ) and ( 3 ) in various ways (see, [6,7]). For more in this direction, see [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

Iqbal,

Saleem,

Iqbal

et al. 2023

Fractal Fract

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In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results.

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“…In 2017, Jain et al [6] introduced a new type of inequality having cubic terms of d(x, y) that extended and generalized the results of Alber and Gueree-Delabriere [2] and others cited in the literature of fixed point theory. See [1,3,7,10,11] for more information on fixed point theory.…”

Section: Introductionmentioning

confidence: 99%

Variants of R-weakly commuting mappings satisfying a weak contraction

Jain¹,

Kumar²,

Park³

2021

MMN

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On the Conditions of Fixed-Point Theorems Concerning $$\varvec{F}$$ F -Contractions

Cited by 4 publications

References 7 publications

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

Variants of R-weakly commuting mappings satisfying a weak contraction

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