Fixed point theorem for generalized set-valued contractions on partial metric space

In this paper we generalize some results of fixed point theory to partial metric spaces by using metric methods in the context of a new extension of Ekeland?s variational principle. We provide some corollaries to unify our results with other existing results in the literature along the same vein. Then, we show that our results require existence assumptions weaker than those for some well-known contractive maps, including the ones in the sense of Banach, Ciric, Song, Kannan and Hardy Rogers. Also, we provide some estimates for the distance to the fixed point set in partial metric space. In order to illustrate the strength of our fixed point theorem, we use it in order to derive a new result on coupled fixed points.

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On some generalized contractive maps in partial metric space and related fixed point theorems

Belhenniche

Benahmed

Guran

et al. 2022

Filomat

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Hybrid Mann Viscosity Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities and Fixed Point Problems

Ceng

Yuan

2019

Mathematics

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In the present work, we introduce a hybrid Mann viscosity-like implicit iteration to find solutions of a monotone classical variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities and a problem of common fixed points of an asymptotically nonexpansive mapping and a countable of uniformly Lipschitzian pseudocontractive mappings in Hilbert spaces, which is called the triple hierarchical constrained variational inequality. Strong convergence of the proposed method to the unique solution of the problem is guaranteed under some suitable assumptions. As a sub-result, we provide an algorithm to solve problem of common fixed points of pseudocontractive, nonexpansive mappings, variational inequality problems and generalized mixed bifunction equilibrium problems in Hilbert spaces.

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Fixed point theorem for generalized set-valued contractions on partial metric space

Cited by 2 publications

References 38 publications

On some generalized contractive maps in partial metric space and related fixed point theorems

On some generalized contractive maps in partial metric space and related fixed point theorems

Hybrid Mann Viscosity Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities and Fixed Point Problems

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