Fixed point theorem in ordered Banach spaces and applications to matrix equations

Mouhadjer, Lotfi; Benahmed, Boubakeur

doi:10.1007/s11117-016-0396-2

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“…This theory and its applications in orederd Banach spaces have been considered by many researchers. (see [2,3,5,6,11,14,16,17] and the references therein. )…”

Section: Introductionmentioning

confidence: 99%

Fixed Points of Non-Smooth Functions on Finite Dimensional Ordered Banach Spaces via Clarke Generalized Jacobian

Zohari

Mardanbeigi

2019

ijaa

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Considering Lipschitz functions which are not necessarily Fréchet differentiable, we obtain a non-smooth version of Lakshmikantham's theorem in finite dimensional ordered Banach spaces . We also present an application of the obtained result in dynamical Coulomb friction problem. Recently, Lakshmikantham et al. [14] have proved some fixed point theorems in ordered Banach space X for a Fréchet differentiable mapping T : X → X. They showed the applications of their results in ODE initial value problems and semilinear parabolic initial boundary value problems. Vijesh and Kumar [19] and Mouhadjer and Benahmed [16] obtained some generalizations of Lakshmikantham's fixed point theorems.

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“…This theory and its applications in orederd Banach spaces have been considered by many researchers. (see [2,3,5,6,11,14,16,17] and the references therein. )…”

Section: Introductionmentioning

confidence: 99%

Fixed Points of Non-Smooth Functions on Finite Dimensional Ordered Banach Spaces via Clarke Generalized Jacobian

Zohari

Mardanbeigi

2019

ijaa

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show abstract

Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

Ninsri

Sintunavarat

2018

J. Fixed Point Theory Appl.

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Investigation of positive definite solution of nonlinear matrix equation $$X^{p}=Q +\sum \nolimits _{i=1}^m A_i^*X^{\delta }A_i$$

Jin

Zhai

2021

Comp. Appl. Math.

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Fixed point theorem in ordered Banach spaces and applications to matrix equations

Cited by 5 publications

References 13 publications

Fixed Points of Non-Smooth Functions on Finite Dimensional Ordered Banach Spaces via Clarke Generalized Jacobian

Fixed Points of Non-Smooth Functions on Finite Dimensional Ordered Banach Spaces via Clarke Generalized Jacobian

Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

Investigation of positive definite solution of nonlinear matrix equation $$X^{p}=Q +\sum \nolimits _{i=1}^m A_i^*X^{\delta }A_i$$

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