Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skiiMann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings Tt : C → C. Each of Tt is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt : C → [0,∞) such that ...

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...

In this paper, we study some new inequalities of Hadamard’s Type for Lipschitzian mappings. some applications are also included.

We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of optimal trajectories, and the answer to it is crucial for closing the gap between the conditions arising in the existence theory and necessary optimality condit...

In this paper, we study several new inequalities of Hadamard’s type for Lipschitzian mappings.

Inequalities are obtained using P0-simple functionals. Applications to Lipschitzian mappings are given.

We establish the convergence of Krasnoselskij iteration for various classes of non-Lipschitzian operators .

This paper aims at deriving and proving some Lipschitzian type error bounds for convex conic problems in a simple way First it is shown that if the recession directions satisfy Slater s condition then a global Lipschitzian type error bound holds Alternatively if the feasible region is bounded then the ordinary Slater condition guarantees a global Lipschitzian type error bound These can be consi...