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- W2054149849 abstract "Let E be a real normed linear space, K be a nonempty subset of E and T:K→E be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., F(T):={x∈K:Tx=x}≠Φ, and there exist x∗∈F(T) and a strictly increasing function Φ:[0,∞)→[0,∞), Φ(0)=0 such that for all x∈K, there exists j(x−x∗)∈J(x−x∗) such that 〈Tx−x∗,j(x−x∗)〉⩽‖x−x∗‖2−Φ(‖x−x∗‖). If y∗∈K is a fixed point of T, then y∗=x∗ and so T has at most one fixed point in K. Suppose there exists x0∈K, such that the sequence {xn} defined by xn+1=anxn+bnTxn+cnun,∀n⩾0, is contained in K, where {an}, {bn} and {cn} are real sequences satisfying the following conditions: an+bn+cn=1; ∑n=0∞(bn+cn)=∞; ∑n=0∞(bn+cn)2<∞; ∑n=0∞cn<∞; and {un} is a bounded sequence in E. Then {xn} converges strongly to x∗. In particular, if y∗ is a fixed point of T in K, then {xn} converges strongly to y∗." @default.
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- W2054149849 date "2005-03-01" @default.
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- W2054149849 title "Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings" @default.
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- W2054149849 doi "https://doi.org/10.1016/j.jmaa.2004.08.060" @default.
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