Convergence theorems for uniformly quasi-Lipschitzian mappings

Convergence theorems for uniformly quasi-Lipschitzian mappings

Convergence Theorems For Two Finite Families of Uniformly L-Lipschitzian Mappings

convergence theorems for two finite families of uniformly l-lipschitzian mappings

ACTA UNIVERSITATIS APULENSIS No 20/2009 CONVERGENCE THEOREMS FOR UNIFORMLY L-LIPSCHITZIAN ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

LetK be a nonempty closed convex subset of a real Banach space E, T : K → K a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n≥0 ⊂ [1,∞), lim n→∞ kn = 1 such that p ∈ F (T ) = {x ∈ K : Tx = x}. Let {an}n≥0, {bn}n≥0 , {cn}n≥0 be real sequences in [0, 1] satisfying the following conditions: (i) an + bn + cn = 1; (ii) ∑ n≥0 bn =∞; (iii) cn = o(bn); (iv) lim n→∞...

The Convergence Theorems for Common Fixed Points of Uniformly L-lipschitzian Asymptotically Φ-pseudocontractive Mappings

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...