On fixed point theorems of mixed monotone operators.
On Krasnoselskii's cone fixed point theorem.
On monotone minimal cuscos
On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces.
On Pseudo-monotone Operators and Nonlinear Noncoercive Variational Problems on Unbounded Domains.
On solvability of mixed monotone operator equations with applications to mixed quasimonotone differential systems involving discontinuities.
On the Approximative Roots of Maximal Monotone Mappings
On the iterative process of solving nonlinear operator equations in PTL-spaces
On the monotone convergence of implicit Newton-like methods.
On the Rockafellar theorem for -monotone multifunctions
Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let be a cyclic -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the -subdifferential of f, .
Positive fixed point of strict set contraction operators on ordered Banach spaces and applications.
Regular Splittings and Monotone Iteration Functions.
Regularization inertial proximal point algorithm for monotone hemicontinuous mapping and inverse strongly monotone mappings in Hilbert spaces.
Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions
We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on -almost everywhere Fréchet differentiability of Lipschitz functions on (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at -almost every at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are -almost everywhere Fréchet differentiable....
Renormalization contracts on nested fractals.
Singular perturbations for a class of quasi-linear hyperbolic equations
Some algebraic fixed point theorems for multi-valued mappings with applications
In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.
Some fixed point theorems for multivalued maps in ordered Banach spaces and applications.
Some fixed points theorems for multi-valued weakly uniform increasing operators
Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods
First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved.