• East Asian mathematical journal
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• 제26권3호
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• 대한수학회논문집
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• 제34권3호
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• pp.771-782
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• 2019

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.269-294
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• 2023

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.

• International Journal of CAD/CAM
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• 제8권1호
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• pp.29-36
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• 2009

Domain mapping is a bijective transformation of one domain to another, usually from a complicated general domain to a chosen convex domain. This is directly useful in many application problems like shape modeling, morphing, texture mapping, shape matching, remeshing, path planning etc. A new approach considering the domain as made up of structural elements, like membranes or trusses, is developed and implemented using the nonlinear finite element formulation. The mapping is performed in two stages, boundary mapping and inside mapping. The boundary of the 3-D domain is mapped to the surface of a convex domain (in this case, a sphere) in the first stage and then the displacement/distortion of this boundary is used as boundary conditions for mapping the interior of the domain in the second stage. This is a general method and it develops a bijective mapping in all cases with judicious choice of material properties and finite element analysis. The consistent global parameterization produced by this method for an arbitrary genus zero closed surface is useful in shape modeling. Results are convincing to accept this finite element structural approach for domain mapping as a good method for many purposes.

• East Asian mathematical journal
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• 제24권1호
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.933-951
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• 2015

In this paper, we consider the problem of convergence of an iterative algorithm for a general system of variational inequalities, a nonexpansive mapping and an ${\eta}$-strictly pseudo-contractive mapping. Strong convergence theorems are established in the framework of real Banach spaces.

• 대한수학회논문집
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• 제29권1호
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• pp.83-95
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• 2014

In a uniformly convex Banach space, we introduce a iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings and utilize a new inequality to prove several convergence results for the iterative sequence. The results generalize and unify many important known results of relevant scholars.

• 대한수학회논문집
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• 제31권3호
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• 대한수학회지
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• 제41권1호
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• pp.131-143
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• 2004

Let Ε and F be locally convex spaces over C. We assume that Ε is a nuclear space and F is a Banach space. Let f be a holomorphic mapping from Ε into F. Then we show that f is of uniformly bounded type if and only if, for an arbitrary locally convex space G containing Ε as a closed subspace, f can be extended to a holomorphic mapping from G into F.