Coupled fixed point theorems in partially ordered metric spaces via mixed g-monotone property

Hazarika, Bipan; Arab, Reza

doi:10.1007/s11784-018-0638-y

Cited by 12 publications

(2 citation statements)

References 16 publications

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“…It is impossible to summarize all generalizations of the ideas of coupled fixed points for mixed monotone maps in partially ordered metric spaces. The investigation on the subject continuous as seen [1,19,22,29], which is far from exhausting the most recent results. Another kind of maps considered in partially ordered complete metric spaces are for monotone maps without the mixed monotone property [13,20].…”

Section: Introductionmentioning

confidence: 98%

A variational principle, coupled fixed points and market equilibrium

Kabaivanov

Zlatanov

2021

NAMC

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We present a possible kind of generalization of the notion of ordered pairs of cyclic maps and coupled fixed points and its application in modelling of equilibrium in oligopoly markets. We have obtained sufficient conditions for the existence and uniqueness of coupled fixed in complete metric spaces. We illustrate one possible application of the results by building a pragmatic model on competition in oligopoly markets. To achieve this goal, we use an approach based on studying the response functions of each market participant, thus making it possible to address both Cournot and Bertrand industrial structures with unified formal method.We show that whenever the response functions of the two players are identical, then the equilibrium will be attained at equal levels of production and equal prices. The response functions approach makes it also possible to take into consideration different barriers to entry. By fitting to the response functions rather than the profit maximization of the payoff functions problem we alter the classical optimization problem to a problem of coupled fixed points, which has the benefit that considering corner optimum, corner equilibrium and convexity condition of the payoff function can be skipped.

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Section: Introductionmentioning

confidence: 98%

A variational principle, coupled fixed points and market equilibrium

Kabaivanov

Zlatanov

2021

NAMC

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“…It is impossible to summarize all generalizations of the ideas of coupled fixed points, for mixed monotone maps, in partially ordered metric spaces. The investigation on the subject continuous as seen [2,15,21], which is far from exhausting the most recent results. Another kind of maps considered in partially ordered complete metric spaces are for monotone maps without the mixed monotone property [7,8,17,22].…”

Section: Introductionmentioning

confidence: 99%

Coupled Fixed Points Results for Hardy–rogers Type of Maps With the Mixed Monotone Property Obtained With the Help of a Variational Technique

AJETI¹,

Zlatanov²

2022

MATTEX 2022, CONFERENCE PROCEEDINGS, Volume 1

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Sufficient conditions have been obtained for the existence and uniqueness of coupled fixed points for Hardy-Rodgers maps with the mixed monotone property in partially ordered metric spaces using a variational technique. The obtained result generalizes and enriches already known results for other types of maps with mixed monotone property. It is shown that in partially ordered metric spaces the maps of Hardy-Rodgers and Reich with mixed monotonic properties do not coincide.

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Modified general splitting method for the split feasibility problem

Vong,

Yao

2024

J Glob Optim

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Coupled fixed point theorems in partially ordered metric spaces via mixed g-monotone property

Cited by 12 publications

References 16 publications

A variational principle, coupled fixed points and market equilibrium

A variational principle, coupled fixed points and market equilibrium

Coupled Fixed Points Results for Hardy–rogers Type of Maps With the Mixed Monotone Property Obtained With the Help of a Variational Technique

Modified general splitting method for the split feasibility problem

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