Strong Convergence of Two Proximal Point Algorithms with Possible Unbounded Error Sequences
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DOI: 10.1007/s10957-016-1028-5
Abstract: We consider a proximal point algorithm with errors for a maximal monotone operator in a real Hilbert space, previously studied by Boikanyo and Morosanu, where they assumed that the zero set of the operator is… read more here.
Keywords: error; proximal point; point; operator ... See more keywords
A New Double-Projection Method for Solving Variational Inequalities in Banach Spaces
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-018-1228-2
Abstract: In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method, which combines Halpern’s technique and the subgradient extragradient idea, is given. Under… read more here.
Keywords: banach spaces; spaces new; method; variational inequalities ... See more keywords
On the Strong Convergence of Subgradients of Convex Functions
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DOI: 10.1007/s10957-018-1276-7
Abstract: In this paper, results on the strong convergence of subgradients of convex functions along a given direction are presented; that is, the relative compactness (with respect to the norm) of the union of subdifferentials of… read more here.
Keywords: convergence subgradients; subgradients convex; strong convergence; convex functions ... See more keywords
On Consequences of the Strong Convergence in Lebesgue–Orlich Spaces
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-4075-7
Abstract: We study the continuity in the sense of the strong topology for the flux function υ → l(υ) = |υ|p(⋅) − 2υ acting from the Lebesgue–Orlicz space Lp(⋅)(Ω, ℝm) to the dual Lp ′ (⋅)(Ω, ℝm), where p′(⋅) is the Hölder-conjugate exponent, under the assumption… read more here.
Keywords: left upsilon; upsilon right; consequences strong; strong convergence ... See more keywords
Weak and strong convergence theorems for solving pseudo-monotone variational inequalities with non-Lipschitz mappings
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DOI: 10.1007/s11075-019-00780-0
Abstract: The aim of this paper is to study a classical pseudo-monotone and non-Lipschitz continuous variational inequality problem in real Hilbert spaces. Weak and strong convergence theorems are presented under mild conditions. Our methods generalize and… read more here.
Keywords: pseudo monotone; convergence theorems; non lipschitz; weak strong ... See more keywords
On the Strong Convergence of Forward-Backward Splitting in Reconstructing Jointly Sparse Signals
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DOI: 10.1007/s11228-021-00603-2
Abstract: We consider the problem of reconstructing a set of sparse vectors sharing a common sparsity pattern from incomplete measurements. To take account of the joint sparsity and promote the coupling of nonvanishing components, we employ… read more here.
Keywords: convergence forward; forward backward; backward splitting; jointly sparse ... See more keywords
A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Fixed Point Theory and Applications"
DOI: 10.1007/s11784-017-0472-7
Abstract: Our interest in this paper is to prove a strong convergence result for finding a zero of the sum of two monotone operators, with one of the two operators being co-coercive using an iterative method… read more here.
Keywords: result involving; monotone; strong convergence; convergence result ... See more keywords
Strong convergence of a forward–backward splitting method with a new step size for solving monotone inclusions
Sign Up to like & getrecommendations! Published in 2019 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-019-0855-z
Abstract: In this paper, our interest is in investigating the monotone inclusion problems in the framework of real Hilbert spaces. To solve this problem, we propose a new modified forward–backward splitting method using the viscosity method… read more here.
Keywords: forward backward; backward splitting; strong convergence; splitting method ... See more keywords
Strong convergence of the split-step theta method for neutral stochastic delay differential equations ☆
Sign Up to like & getrecommendations! Published in 2017 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2017.05.008
Abstract: Abstract Neutral stochastic delay differential equations often appear in various fields of science and engineering. The aim of this article is to investigate the strong convergence of the split-step theta (SST) method for the neutral… read more here.
Keywords: stochastic delay; neutral stochastic; delay; differential equations ... See more keywords
A necessary and sufficient condition for strong convergence in Sobolev spaces
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.07.012
Abstract: Abstract We present an improved version of a necessary and sufficient condition for strong convergence in the Sobolev space W 1 , p ( Ω ) and provide a nontrivial application to a class of… read more here.
Keywords: sufficient condition; necessary sufficient; condition strong; strong convergence ... See more keywords
A note on strong convergence of implicit scheme for SDEs under local one-sided Lipschitz conditions
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DOI: 10.1080/00207160.2020.1737861
Abstract: In this paper, we aim to study strong convergence of theta-EM scheme for stochastic differential equations under a local one-sided Lipschitz condition. Since the existence and uniqueness of theta-EM solution cannot be guaranteed under the… read more here.
Keywords: local one; one sided; sided lipschitz; scheme ... See more keywords