Positive fixed points for a class of nonlinear operators and applications

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

“…where Q is a positive semi definite matrix, A i are arbitrary square matrices, f i are Löwner-Heinz monotone operators and g is an Uchiyama operator [16][17][18]. Our results improve, extend and generalize some existing ones in the literature [11,15,19,20]. Furthermore, we provide two algorithms involving the Newton-Raphson method for solving new classes of nonlinear matrix equations.…”

“…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.…”

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

“…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. )…”

Positive solutions to a class of random operator equations and applications to stochastic integral equations

“…Nonlinear operator equations defined on Banach spaces play an important role in the theory of differential and integral equations and have been extensively studied over the past several decades (see [1][2][3][4][5][6][7]).…”