Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

Abass, H. A.; Oyewole, O. K.; Jolaoso, L. O.; Aremu, K. O.

doi:10.1080/00036811.2023.2256357

Cited by 5 publications

(1 citation statement)

References 38 publications

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“…al. [11], many authors have introduced different iterative algorithms being Halpern, Viscosity, Mann, Kranoselski, Parallel, Cylic, Hybrid to mention a few to approximate solutions of fixed point problems both in Hilbert spaces and Banach spaces, (see [1][2][3][4][5][6]9,14,15,20] and the references contained in).…”

Section: Introductionmentioning

confidence: 99%

Generalized viscosity method for approximating solutions of countable families of certain nonlinear mappings in real Hilbert space

ABASS

2024

MATHEMATICA

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The purpose of this paper is to introduce a three step iterative algorithm which include a general viscosity explicit method for approximating a common solution of fixed point problem of an infinite family of k_i-demimetric mapping and a directed operator in the framework of real Hilbert space. Furthermore, we prove a strong convergence theorem for approximating a common solution of the aforementioned problems. We also show that our iterative algorithm holds for an infinite family of L-Lipschitzian and quasi-pseudocontractive mapping together with a directed operator. The iterative algorithm presented in this article is design in such a way that it solves some variational inequality problem and no compactness condition is impose on our scheme and mapping. Finally, we give applications of our main result to variational inclusion and equilibrium problems. Our result complements and extends some related result in literature.

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Section: Introductionmentioning

confidence: 99%

Generalized viscosity method for approximating solutions of countable families of certain nonlinear mappings in real Hilbert space

ABASS

2024

MATHEMATICA

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Self-adaptive Technique with Double Inertial Steps for Inclusion Problem on Hadamard Manifolds

Abass,

Oyewole,

Aremu

et al. 2024

J. Oper. Res. Soc. China

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In this article, we investigate monotone and Lipschitz continuous variational inclusion problem in the settings of Hadamard manifolds. We propose a forward–backward method with a self-adaptive technique for solving variational inclusion problem. To increase the rate of convergence of our proposed method, we incorporate our iterative method with double inertial steps and establish a convergence result of our iterative method under some mild conditions. Finally, in order to illustrate the computational effectiveness of our method, some numerical examples are also discussed. The result present in this article is new in this space and extends many related results in the literature.

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An algorithmic approach to solving split common fixed point problems for families of demicontractive operators in Hilbert spaces

Abass,

Aphane

2023

Boll Unione Mat Ital

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In this article, we propose a new iterative algorithm for solving split common fixed point problems for finite families of single-valued demicontractive mappings in the setting of real Hilbert spaces. In order to solve this problem, we introduce a Halpern method with with an Armijo-line search for approximating the solution of the aforementioned problems. We establish a strong convergence result of the proposed method and display some numerical examples to illustrate the performance of our main result. Our result complements and generalizes some related results in literature.

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Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

Cited by 5 publications

References 38 publications

Generalized viscosity method for approximating solutions of countable families of certain nonlinear mappings in real Hilbert space

Generalized viscosity method for approximating solutions of countable families of certain nonlinear mappings in real Hilbert space

Self-adaptive Technique with Double Inertial Steps for Inclusion Problem on Hadamard Manifolds

An algorithmic approach to solving split common fixed point problems for families of demicontractive operators in Hilbert spaces

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