Results 51 to 60 of about 604,834 (284)

Uniform convexity and the splitting problem for selections [PDF]

J. Math. Anal. Appl. 360:1 (2009), 307-316, 2009
We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not ...
arxiv   +1 more source

Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces

Abstract and Applied Analysis, 2013
We introduce Mann-type viscosity approximation methods for finding solutions of a multivalued variational inclusion (MVVI) which are also common ones of finitely many variational inequality problems and common fixed points of a countable family of ...
Lu-Chuan Ceng, Abdul Latif, Abdullah E. Al-Mazrooei   +2 more
doaj   +1 more source

Directional Differentiability of the Metric Projection in Uniformly Convex and Uniformly Smooth Banach Spaces [PDF]

arXiv, 2023
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. Let Pc from X to C denote the (standard) metric projection operator. In this paper, we define the Gateaux directional differentiability of Pc. We investigate some properties of the Gateaux directional differentiability of Pc. In particular,
arxiv  

Convergence theorems for generalized nonexpansive mappings in uniformly convex Banach spaces

, 2015
In this paper, we prove strong and weak convergence theorems for a mapping defined on a bounded, closed and convex subset of a uniformly convex Banach space, satisfying the RCSC condition. This condition was introduced by Karapınar (Dynamical Systems and
Dipti Thakur, B. Thakur, M. Postolache
semanticscholar   +1 more source

A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space

, 1974
where H(A, B) denotes the Hausdorff distance between A and B. A point x e C is called a fixed point of T if x e Tx. Fixed point theorems for such mappings T have been established by Mar kin [11] for Hubert spaces, by Browder [2] for spaces having weakly ...
Teck-Cheong Lim
semanticscholar   +1 more source

Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications

Journal of Applied Mathematics, 2013
Two countable families of hemirelatively nonexpansive mappings are considered based on a hybrid projection algorithm. Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space.
Zi-Ming Wang, Poom Kumam
doaj   +1 more source

Simulation of Inhomogeneous Refractive Index Fields Induced by Hot Tailored Forming Components

Advanced Engineering Materials, EarlyView.
This article presents a simulation model for simulating inhomogeneous refractive index fields (IRIF) in hot‐forged components, accounting for thermal influences and complex geometries. Through this simulation, a priori knowledge about the propagation of the IRIF can be obtained, allowing for the positioning of the component or an optical measurement ...
Pascal Kern, Lennart Hinz, Markus Kästner, Eduard Reithmeier   +3 more
wiley   +1 more source

Strong Convergence to a Solution of a Variational Inequality Problem in Banach Spaces

Journal of Applied Mathematics, 2014
We consider the variational inequality problem for a family of operators of a nonempty closed convex subset of a 2-uniformly convex Banach space with a uniformly Gâteaux differentiable norm, into its dual space.
Yasunori Kimura, Kazuhide Nakajo
doaj   +1 more source

Bioinspired Design of Isotropic Lattices with Tunable and Controllable Anisotropy

Advanced Engineering Materials, EarlyView.
This study introduces nested isotropic lattices, integrating architectural elements like nesting orders and orientations inspired by bioarchitectures. The design enables tunable anisotropy across nine mono‐nest and twenty multi‐nest lattices with 252 parametric variations, demonstrating transitions from shear‐ to tensile‐compression‐dominant behaviors ...
Ramalingaiah Boda, Biranchi Panda, Shanmugam Kumar   +2 more
wiley   +1 more source

A Bound for the Modulus of Continuity for Metric Projections in a Uniformly Convex and Uniformly Smooth Banach Space

, 1996
In 1979, Bjornestal obtained a local estimate for a modulus of uniform continuity of the metric projection operator on a closed subspace in a uniformly convex and uniformly smooth Banach spaceB.
Y. Alber
semanticscholar   +1 more source