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1 – 10 of 11Getahun Bekele Wega and Habtu Zegeye
Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The…
Abstract
Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is
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H. Fukhar-ud-din and A.R. Khan
The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and
Abstract
The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and
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In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard…
Abstract
Purpose
In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.
Design/methodology/approach
This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.
Findings
Showed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.
Originality/value
This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.
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Godwin Amechi Okeke and Safeer Hussain Khan
The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued
Abstract
The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued
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Hudson Akewe and Hallowed Olaoluwa
In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to…
Abstract
Purpose
In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that
Design/methodology/approach
The concepts of relative ρ-stability and weak ρ-stability are introduced, and conditions in which these multistep iterations are relatively ρ-stable, weakly ρ-stable and ρ-stable are established for the newly introduced strong ρ-quasi-contractive-like class of maps.
Findings
Noor type, Ishikawa type and Mann type iterative sequences are deduced as corollaries in this study.
Originality/value
The results obtained in this work are complementary to those proved in normed and metric spaces in the literature.
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Godwin Amechi Okeke and Daniel Francis
This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known…
Abstract
Purpose
This paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.
Design/methodology/approach
The results of this paper are theoretical and analytical in nature.
Findings
The authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutlu et al. [1]. An example was constructed to demonstrate the applicability of the results.
Research limitations/implications
Analytical and theoretical results.
Practical implications
The results of this paper can be applied in science and engineering.
Social implications
The results of this paper is applicable in certain social sciences.
Originality/value
The results of this paper are new and will open up new areas of research in mathematical sciences.
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Godwin Amechi Okeke and Daniel Francis
The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors…
Abstract
Purpose
The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.
Design/methodology/approach
The results of this paper are theoretical and analytical in nature.
Findings
The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.
Research limitations/implications
The results are theoretical and analytical.
Practical implications
The results were applied to solving nonlinear integral equations.
Social implications
The results has several social applications.
Originality/value
The results of this paper are new.
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Abubakar Sani Halilu, Arunava Majumder, Mohammed Yusuf Waziri, Kabiru Ahmed and Aliyu Muhammed Awwal
The purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.
Abstract
Purpose
The purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.
Design/methodology/approach
Conjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.
Findings
A conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.
Originality/value
The proposed algorithm is a new approach that will not either submitted or publish somewhere.
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Ioan R. Ciric, Florea I. Hantila and Mihai Maricaru
The purpose of this paper is to present three novel techniques aimed at increasing the efficiency of the polarization fixed point method for the solution of nonlinear periodic…
Abstract
Purpose
The purpose of this paper is to present three novel techniques aimed at increasing the efficiency of the polarization fixed point method for the solution of nonlinear periodic field problems.
Design/methodology/approach
Firstly, the characteristic B‐M resulting from the constitutive relation B‐H is replaced by a relation between the components of the harmonics of the vectors B and M. Secondly, a dynamic overrelaxation method is implemented for the convergence acceleration of the iterative process involved. Thirdly, a modified dynamic overrelaxation method is proposed, where only the relation B‐M between the magnitudes of the field vectors is used.
Findings
By approximating the actual characteristic B‐M by the relation between the components of the harmonics of the vectors B and M, the amount of computation required for the field analysis is substantially reduced. The rate of convergence of the iterative process is increased by implementing the proposed dynamic overrelaxation technique, with the convergence being further accelerated by applying the modified dynamic overrelaxation presented. The memory space is also well reduced with respect to existent methods and accurate results for nonlinear fields in a real world structure are obtained utilizing a normal size processor notebook in a time of about one‐half of one minute when no induced currents are considered and of about one minute when eddy currents induced in solid ferromagnetic parts are also fully analyzed.
Originality/value
The originality of the novel techniques presented in the paper consists in the drastic approximations proposed for the material characteristics of the nonlinear ferromagnetic media in the analysis of periodic electromagnetic fields. These techniques are highly efficient and yield accurate numerical results.
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The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical…
Abstract
Purpose
The purpose of this paper is to develop a viscous-type frequency dependent scalar Preisach hysteresis model and to identify the model using measured data and nonlinear numerical field analysis. The hysteresis model must be fast and well applicable in electromagnetic field simulations.
Design/methodology/approach
Iron parts of electrical machines are made of non-oriented isotropic ferromagnetic materials. The finite element method (FEM) is usually applied in the numerical field analysis and design of this equipment. The scalar Preisach hysteresis model has been implemented for the simulation of static and dynamic magnetic effects inside the ferromagnetic parts of different electrical equipment.
Findings
The comparison between measured and simulated data using a toroidal core shows a good agreement. A modified nonlinear version of TEAM Problem No. 30.a is also shown to test the hysteresis model in the FEM procedure.
Originality/value
The dynamic model is an extension of the static one; an extra magnetic field intensity term is added to the output of the static inverse model. This is a viscosity-type dynamic model. The fixed-point method with stable scheme has been realized to take frequency dependent anomalous losses into account in FEM. This scheme can be used efficiently in the frame of any potential formulations of Maxwell's equations.
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