and Applied Analysis 3 Remark 1.2. i Since 0 αn βn 1, n 1 and ∑∞ n 1 αnβn ∞, the iterative sequence 1.6 could not be reduced to a Mann iterative sequence 1.4 . Therefore, the iterative sequence 1.6 has some particular cases. ii The iterative sequence 1.6 is usually called the Ishikawa iterative sequence. iii Chidume andMutangadura 17 gave an example to show that the Mann iterative sequence fail...

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 .

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let T be an asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we first provide a ergodic retraction theorem and a mean ergodic convergence theorem. Using this result, we show that the set F (T ) of fixed points of T is a sunny, nonexpansive retract of C if the norm of X is u...

Error bounds in approximating the Riemann-Stieltjes integral in terms of some moments of the integrand are given. Applications for p convex functions and in approximating the Finite Foureir Transform are pointed out as well. 1. Introduction In order to approximate the Riemann-Stieltjes integral R b a f (t) du (t) with the arguably simpler expression (1.1) u (b) u (a) b a Z b a f (t) dt; where R...

We present several new results on the asymptotic behavior of firmly nonexpansive mappings in Banach spaces and in the Hubert ball. Let D be a subset of a (real) Banach space X. Recall that a mapping T: D -» X is said to be firmly nonexpansive [2, 4] if for each x and y in D, the convex function /: [0,1] -> [0, oo) defined by f{s) = \(\-s)x + sTx-((l-s)y + sTy) \ is nonincreasing. Note that T is...