Inertial Accelerated Algorithm for Fixed Point of Asymptotically Nonexpansive Mapping in Real Uniformly Convex Banach Spaces

Harbau, M. H.; Ugwunnadi, Godwin Chidi; Jolaoso, Lateef Olakunle; Abdulwahab, Ahmad

doi:10.3390/axioms10030147

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…Our Theorem 1 provides generalizations and improvements on the results of Khan et al [44] in the following ways: In Khan et al [44], systems of classical equilibrium problems (), which are special cases of the problems described in () and finite family of demicontractive mappings are considered, while in our result, systems of generalized mixed equilibrium problems () and a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense are studied. Apart from determining solutions to fixed point and equilibrium problems by the Algorithm of Khan et al [44], our scheme is also used to approximate zeros of a family of mappings satisfying (). Unlike the algorithm of Khan et al [44], our algorithm () has an inertial term, which is well‐known and frequently used in developing fast convergence schemes (see earlier studies [40, 52–54] and the references therein). …”

Section: Discussionmentioning

confidence: 85%

“…3. Unlike the algorithm of Khan et al [44], our algorithm (36) has an inertial term, which is well-known and frequently used in developing fast convergence schemes (see earlier studies [40,[52][53][54] and the references therein).…”

Section: Discussionmentioning

confidence: 99%

“…In a similar fashion, combining (43), (53), and (58) and the fact that for each i ≥ 1, r i < 𝛼 i , we have lim…”

Section: Assume That Conditions (I)-(v) Of Lemma 3 and The Following ...mentioning

confidence: 90%

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Inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

Ahmad,

Kumam,

Harbau

et al. 2024

Math Methods in App Sciences

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In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result.

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Section: Discussionmentioning

confidence: 85%

Section: Discussionmentioning

confidence: 99%

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Inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

Ahmad,

Kumam,

Harbau

et al. 2024

Math Methods in App Sciences

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“…Under these conditions, an analysis of the computational performance of each one of the algorithms presented was carried out (based on the outlines of [28][29][30][31] to validate the performance of algorithms). The hardware overload degree of the machine resources (CPU and memory) was computed, estimating the time of use of the microprocessor and the amount of memory used for the execution of each one of the procedures defined in Appendix C. In addition, the value of real time invested by the machine was calculated for the methods presented in Section 3.…”

Section: Analysis Of the Computational Performancementioning

confidence: 99%

Some New Symbolic Algorithms for the Computation of Generalized Asymptotes

et al. 2022

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We present symbolic algorithms for computing the g-asymptotes, or generalized asymptotes, of a plane algebraic curve, C, implicitly or parametrically defined. The g-asymptotes generalize the classical concept of asymptotes of a plane algebraic curve. Both notions have been previously studied for analyzing the geometry and topology of a curve at infinity points, as well as to detect the symmetries that can occur in coordinates far from the origin. Thus, based on this research, and in order to solve practical problems in the fields of science and engineering, we present the pseudocodes and implementations of algorithms based on the Puiseux series expansion to construct the g-asymptotes of a plane algebraic curve, implicitly or parametrically defined. Additionally, we propose some new symbolic methods and their corresponding implementations which improve the efficiency of the preceding. These new methods are based on the computation of limits and derivatives; they show higher computational performance, demanding fewer hardware resources and system requirements, as well as reducing computer overload. Finally, as a novelty in this research area, a comparative analysis for all the algorithms is carried out, considering the properties of the input curves and their outcomes, to analyze their efficiency and to establish comparative criteria between them.

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