Coincidence point theorems in ordered Banach spaces and applications

Berzig, Maher; Bouali, Marwa

doi:10.1007/s43037-019-00007-3

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2020

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Cited by 2 publications

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“…The coincidence point theory is a powerful tool in nonlinear analysis for solving a wide range of nonlinear equations arising from various applications in engineering, economics and mechanics, see for instance [1][2][3][4][5][6][7][8]. In particular, nonlinear equations in Banach spaces involving α-concave and α (− )-convex operators are considered in [9][10][11][12][13][14][15] and some references therein.…”

Section: Introductionmentioning

confidence: 99%

Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

2020

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Consider an ordered Banach space and f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f(X)=g(X) has a positive solution, whenever f is strictly \alpha -concave g-monotone or strictly (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

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