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Homotopy Algorithms for Engineering Analysis
Published in Hojjat Adeli, Supercomputing in Engineering Analysis, 2020
Layne T. Watson, Manohar P. Kamat
A function is called uniformly convex if it is convex and its Hessian’s smallest eigenvalue is bounded away from zero. Consider next the constrained optimization problem minx≥0 f(x)
Exponential decay and blow-up results for a viscoelastic equation with variable sources
Published in Applicable Analysis, 2023
Nhan Cong Le, Truong Xuan Le, Y. Van Nguyen
Let Ω be a bounded domain in with smooth boundary . Throughout this section, we assume that is a measurable function. We define the Lebesgue space with a variable exponent which is the so-called Nakano space and a special case of Musielak–Orlicz spaces (see [28]), as follows: The space is equipped with the Luxemburg-type norm is separable and uniformly convex Banach space. The following proposition shows the relation between the norm and the modular .
Simplified Levenberg–Marquardt method in Banach spaces for nonlinear ill-posed operator equations
Published in Applicable Analysis, 2023
Pallavi Mahale, Farheen M. Shaikh
Let X be uniformly convex and uniformly smooth space and let Y be uniformly smooth space.Let Equation (1) has a solution and there exist a small number such that where i.e. domain of F, is a closed and convex subset of X with not empty interior and is an initial approximation for the exact solution such that .There exists a family of linear operators such that is continuous on There exist a constant such that for all .
Single Bregman projection method for solving variational inequalities in reflexive Banach spaces
Published in Applicable Analysis, 2022
Lateef O. Jolaoso, Yekini Shehu
Let E be a real Banach space and The modulus of convexity of E is the function defined by The space E is said to be uniformly convex if for any strictly convex if for all with and p-uniformly convex if there exists such that for all When we say that E is 2-uniformly convex. It is obvious that every p-uniformly convex Banach space is uniformly convex. More so, we say that E is smooth if the limit exists for and uniformly smooth if the limit (12) is attained uniformly for The Hilbert and Lebesgue () are 2-uniformly convex and uniformly smooth Banach spaces.