A5043769044- Advanced Banach Space Theory
- Holomorphic and Operator Theory
- Advanced Operator Algebra Research
- Functional Equations Stability Results
- Approximation Theory and Sequence Spaces
- Fixed Point Theorems Analysis
- Optimization and Variational Analysis
- Advanced Harmonic Analysis Research
- Advanced Topics in Algebra
- Numerical methods for differential equations
- Mathematical and Theoretical Analysis
- Gastroesophageal reflux and treatments
- Point processes and geometric inequalities
- Mathematical Analysis and Transform Methods
- Algebraic and Geometric Analysis
North China Electric Power University
2020-2024
Xiamen University
2016-2019
AbstractAbstractAssume that X, Y are real Banach spaces, has uniform convexity of type p (≥ 1), and f: X → is a standard coarse isometry. In this paper, we show ifthen there linear isometry U : so thatwhere defined byRepresentation properties isometries in free ultrafilter limits on also discussed.Mathematics Subject Classification (2010): Primary 46B0446B2047A58Secondary 46A20Key words: Coarse isometrystabilityuniform convexityBanach space
We study the stability of approximative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:math>-compactness, where<mml:math id="M2"><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:math>is norm or weak topology. Let<mml:math id="M3"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow></mml:math>be an index set and for every<mml:math id="M4"><mml:mi>λ</mml:mi><mml:mo>∈</mml:mo><mml:mi...
In this paper, we show that the sum of a compact convex subset and simultaneously $\tau$-strongly proximinal (resp. approximatively $\tau$-compact subset) Banach space X is ), weakly still compact, where $\tau$ norm or weak topology. Moreover, some related results on subspaces are presented.
Abstract Let be two Banach spaces, an ‐norm‐additive map for some , that is, In this paper, we prove if is surjective with then there exists a linear isometry such The estimate sharp. We also approximate standard maps between the positive cones of continuous function spaces by isometries within sharp approximation error .
Abstract Let $X, Y$ be two locally compact Hausdorff spaces and $T:C_0(X)\rightarrow C_0(Y)$ a standard surjective ɛ -norm-additive map, i.e. \begin{equation*} \big|\|T(f)+T(g)\|-\|f+g\|\big|\leq \varepsilon,\;{\rm for\;all}\; f, g\in C_0(X). \end{equation*} Then there exist homeomorphism $\varphi:Y\rightarrow X$ continuous function $\lambda:Y\rightarrow\lbrace\pm1\rbrace$ such that |T(f)(y)-\lambda(y)f(\varphi(y))|\leq\frac{3}{2}\varepsilon,\;{\rm for\;all}\;y\in Y,\;f\in The estimate ‘...
UDC 517.5 We prove the generalized stability of functional equations <mml:math> <mml:mrow> <mml:mo>‖</mml:mo> <mml:mi>f</mml:mi> <mml:mo form="prefix">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:mi>y</mml:mi> form="postfix">)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> </mml:math> and <mml:mo>-</mml:mo> in <mml:mi>p</mml:mi> </mml:math>-uniformly convex spaces with <mml:mo>≥</mml:mo> <mml:mn>1.</mml:mn>
В заметке рассматривается слабая стабильность симметризации $\Theta=(f( \boldsymbol\cdot )-f(- ))/2$ общей $\varepsilon$-изометрии $f\colon X \to Y$ из одного банахова пространства в другое. частности, получен следующий, определенном смысле неожиданный, результат о слабой стабильности: для каждого $x^\ast\in X^\ast$ найдется $\varphi\in Y^\ast$, такой, что $\|\varphi\|=\|x^\ast\|:= r$ и $$ |\langle x^\ast,x\rangle-\langle \varphi,\Theta(x)\rangle|\le\tfrac{3}{2}r\varepsilon\quad{для всех }...
In this paper, we show that the sum of a compact convex subset and simultaneously $\tau$-strongly proximinal (resp. approximatively $\tau$-compact subset) Banach space X is tau-strongly ), weakly still compact, where $\tau$ norm or weak topology. Moreover, some related results on subspaces are presented.
A weak stability bound for the $\varepsilon$-isometry $f$ form positive cone of a reflexive, strictly convex and Gateaux smooth Banach lattice $X$ to space $Y$ is presented. This result used prove theorem $f:(\mathbb{R}^n)^+\rightarrow Y$, where $\mathbb{R}^n$ $n$-dimensional equipped with $1$-unconditional norm n-dimensional, space.
Пусть $K$ компактное хаусдорфово пространство, $C(K)$-вещественное банахово пространство всех непрерывных функций на $K$, снабженное равномерной нормой, и $C(K)^+$ - положительный конус в $C(K)$. В статье будет получен следующий результат о слабой устойчивости симметризации $\Theta=(f( \boldsymbol\cdot )-f(-\;\boldsymbol\cdot )/2$ l $\varepsilon$-изометрии общего вида $f$ из $C(K)^+\cup-C(K)^+$ $Y$: для любого элемента $k\in K$ существует такой $\phi\in S_{Y^\ast}$, что \begin{equation*}...