Chidume C E,Chidume C O.Convergence theorem for fixed points of uniformly continuous generalized phi-hemicontractive mappings. Journal of Mathematical Analysis and Applications . 2005C. E. Chidume and C. O. Chid
In Theorem 2.11 a further generalization is obtained for a complete Menger space (S,F,T), where T belongs to a more general class of continuous t-norms than in the previous case where T=T M (=min). Theorem 3.2 is a generalization of Theorem 2 from [2]. Thereafter the notion of a...
Theorem 2 [13] Let \phi :I=\left [ \sigma ,\rho \right ] \subset \mathbb{R} \longrightarrow \mathbb{R} be an absolutely continuous mapping on I^{\circ } such that \phi ^{{\prime }}\in L_{1}\left ( \left [ \sigma ,\rho \right ] \right ) , where \sigma ,\rho \in...
Nonlinear Analysis Fixed point theorem for generalized 桅 -pseudocontractive mappingsStrongly pseudocontractive mapping0-strongly pseudocontractive mappingGeneralizedφ-pseudocontractive mappingFixed pointLet E be a real Banach space, C be a nonempty closed convex subset of E and T : C→ C be...
Theorem 1.6 Under the assumptions of Theorem 1.4, there exists a unique continuous mapping γ from R+n+1 to Rn such thatγ(x,t)=x+∫0tu(γ(x,τ),τ)dτand|γ(x1,t)−γ(x2,t)|≤C|x1−x2|1−Cεexp(Cεt)for all t>0 and |x1−x2|≤1. The rest of this paper ...
A classical best approximation theorem was introduced by Fan [13]; that is, if A is a nonempty compact convex subset of a Hausdorff locally convex topological vector space B and T : A→ B is a continuous mapping, then there exists an element x∈ A such that d(x, Tx) = d(Tx, A)...
Let \(F: X\rightarrow2^{Z}\) be a continuous set-valued mapping with compact values. Then the set-valued mapping $$\Gamma(x)= \operatorname {Max}_{w} F(x) $$ is nonempty closed and upper semicontinuous. In the sequel we need the following alternative theorem which is a variant...
Theorem 3.1 Assume that Y is an S-subset of itself. Let the following conditions hold ThenT(S(Y))¯∩⋂y∈YF(y)≠0̸. Proof We define a new set-valued mapping F̂:Y→2T(S(Y))¯ by, for y∈Y, F̂(y)=T(S(Y))¯∩cclF(y). Then F̂ has clearly closed values...
Theorem 5 Let K be a nonempty closed convex subset of a real Banach space E . Let T:K→K be a generalized Lipschitz pseudo-contractive mapping such that ≔F(T)≔{x∈K:Tx=x}≠0̸ . Let {αn}n≥1,{λn}n≥1 and {θn}n≥1 be real sequences in (0,1) such that αn...
semi-continuous mapping 半连续映射【胭抽.以扣伪.曰旧叮口n那堪;nO月yUe即ePu一。oe oo6p‘eH“e],粤(下)(uP衅(fo‘))半浮等映射’‘拓扑空间(top01o卿sPace)x到偏序集尸的映射f,使得 U川戈.=x蕴含 而了(x。)簇f(x)〔垫f(x,)》f(、)],这里,而(迹)表示上(下)极限. M.H.B浦1翼xoBc...