On the zero point problem of monotone operators in Hadamard spaces

Eskandani, G. Zamani; Raeisi, M.

doi:10.1007/s11075-018-0521-3

Cited by 27 publications

(15 citation statements)

References 41 publications

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“…Then, (R 2 , d X ) is a complete p-uniformly convex metric space with p = 2 and parameter c = 2, and with the geodesic joining x to y given by [45,Example 5.2]).…”

Section: Proposition 1 [14]mentioning

confidence: 99%

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Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Aremu¹,

Izuchukwu²,

Ogwo³

2021

JIMO

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In this paper, we propose and study a multi-step iterative algorithm that comprises of a finite family of asymptotically k i -strictly pseudocontractive mappings with respect to p, and a p-resolvent operator associated with a proper convex and lower semicontinuous function in a p-uniformly convex metric space. Also, we establish the ∆-convergence of the proposed algorithm to a common fixed point of finite family of asymptotically k i -strictly pseudocontractive mappings which is also a minimizer of a proper convex and lower semicontinuous function. Furthermore, nontrivial numerical examples of our algorithm are given to show its applicability. Our results complement a host of recent results in literature.

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“…Then, (R 2 , d X ) is a complete p-uniformly convex metric space with p = 2 and parameter c = 2, and with the geodesic joining x to y given by [45,Example 5.2]).…”

Section: Proposition 1 [14]mentioning

confidence: 99%

“…1 . Then f is a proper convex and lower semicontinuous function in (R 2 , d X ) but not convex in the classical sense (see [45]). We now consider the following 4 cases for our numerical experiments given in…”

Section: Proposition 1 [14]mentioning

confidence: 99%

Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Aremu¹,

Izuchukwu²,

Ogwo³

2021

JIMO

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show abstract

“…Indeed, for all x, y ∈ R Define ϕ 1 : R 2 → R by ϕ 1 (x 1 , x 2 ) = 100((x 2 + 1) − (x 1 + 1) 2 ) 2 + x 2 1 . Then ϕ 1 is a proper convex and lower semicontinuous function in (R 2 , ρ) but not convex in the classical sense (see [49]). Also, define ϕ i : R 2 → R by ϕ i (x 1 , x 2 ) = 50ix 2 1 , i = 2, 3, 4.…”

Section: Suppose Not Then There Exists Ymentioning

confidence: 99%

Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces

Khan

Izuchukwu

Aphane

et al. 2022

NACO

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<p style='text-indent:20px;'>The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.</p>

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“…They proved the relation between the maximality and Minty's surjectivity condition. Zamani Eskandani and Raeisi [13], by using products of finitely many resolvents of monotone operators, proposed an iterative algorithm for finding a common zero of a finite family of monotone operators and a common fixed point of and infinitely countable family of non-expansive mappings in Hadamrd spaces. In this section, we will characterize the notation of monotone relations in Hadamard spaces based on characterization of monotone sets in Banach spaces [7,11,12].…”

Section: Monotone Relationsmentioning

confidence: 99%

Monotone relations in Hadamard spaces

Moslemipour

Roohi

Reza

et al. 2019

Filomat

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In this paper, the notion of W-property for subsets of X × X ♦ is introduced and investigated, where X is an Hadamard space and X ♦ is its linear dual space. It is shown that an Hadamard space X is flat if and only if X × X ♦ has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is proved.

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On the zero point problem of monotone operators in Hadamard spaces

Cited by 27 publications

References 41 publications

Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces

Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces

Monotone relations in Hadamard spaces

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