Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

Waheed, Muhammad Talha; Rehman, Saif Ur; Jan, Naeem; Gumaei, Abdu; Al-Rakhami, Mabrook

doi:10.1155/2021/4144966

Cited by 6 publications

(1 citation statement)

References 27 publications

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“…The first result [1] deals with maps with the mixed monotone property in complete, partially ordered metric spaces. There are a great number of contemporary research papers on the theory of coupled fixed points with the mixed monotone property [2], without the mixed monotone property [3], in ordered probabilistic metric spaces [4], in modular metric spaces [5], in metric spaces endowed with a graph [6], fuzzy cone metric spaces [7], in b-metric spaces [8], and for multi-valued maps [9] . The idea of coupled fixed points was generalized for coupled best-proximity points [10].…”

Section: Introductionmentioning

confidence: 99%

Coupled Fixed Points for Hardy–Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Kabaivanov

Zhelinski²,

Zlatanov³

2022

Symmetry

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In this paper we generalize Hardy–Rogers maps in the context of coupled fixed points. We comment on the symmetry of some of the coefficients involved in the Hardy–Rogers condition, and thus, we deduce a simpler formula. We generalize, with the help of the obtained main theorem, some known results about existence and uniqueness of market equilibrium in duopoly markets. As a consequence, we ascertain that the equilibrium production should be equal for both market participants provided that they have symmetric response functions. With the help of the main theorem, we investigate and enrich some recent results regarding market equilibrium in duopoly markets. We define a generalized response function that includes production and surpluses. Finally, we illustrate a possible application of the main result in the investigation of market equilibrium when the payoff functions are non-differentiable.

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Section: Introductionmentioning

confidence: 99%

Coupled Fixed Points for Hardy–Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Kabaivanov

Zhelinski²,

Zlatanov³

2022

Symmetry

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Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

Rehman

Waheed

Jan

et al. 2021

Journal of Mathematics

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In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.

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Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

Hammad

Aydi

Park

2022

MATH

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<abstract><p>The goal of this manuscript is to obtain some tripled fixed point results under a new contractive condition and triangular property in the context of fuzzy cone metric spaces (F$ _{\text{CM}} $-spaces). Moreover, two examples and corollaries are given to validate our work. Ultimately, as applications, the notion of Lebesgue integral is represented by the fuzzy method to discuss the existence of fixed points. Also, the existence and uniqueness solution for a system of Volterra integral equations are studied by the theoretical results.</p></abstract>

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Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

Cited by 6 publications

References 27 publications

Coupled Fixed Points for Hardy–Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Coupled Fixed Points for Hardy–Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

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