The multiple-sets split equality fixed point problem for countable families of multi-valued demi-contractive mappings

Chidume, C. E.; Ndambomve, Patrice; Bello, A. U.; Okpala, M. E.

doi:10.12988/ijma.2015.412209

Cited by 14 publications

(10 citation statements)

References 15 publications

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“…Also U i is τ i -demicontractive and T j is θ j -demicontractive, where τ i = 2i−1 2i+1 and θ j = j j+1 , then I − U i and I − T j are demiclosed at 0. Indeed, for any i ∈ {1, 2, · · · , p} and j ∈ {1, 2, · · · , q}, similar to the proof of Example 2.5 in [4], we have U i is τ i -demicontractive and T j is θ j -demicontractive. Meanwhile, I − U i is obviously demiclosed at 0.…”

Section: Lemma 32 Given Two Bounded Linear Operatorsmentioning

confidence: 66%

Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings

Ya-qin¹,

Fang²

2017

J. Nonlinear Sci. Appl.

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In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem. The results obtained in this paper generalize and improve the recent ones announced by many others. c 2017 All rights reserved.Keywords: Multiple-set split equality common fixed-point problem, demicontractive mapping, strong convergence. 2010 MSC: 47H09, 47H10, 47J05, 54H25.

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Section: Lemma 32 Given Two Bounded Linear Operatorsmentioning

confidence: 66%

Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings

Ya-qin¹,

Fang²

2017

J. Nonlinear Sci. Appl.

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“…Such a fixed point is proved to be also a solution of variational inequality problem related to quadratic minimization problems. See also Chidume et al ( 2015 ).…”

Section: Introductionmentioning

confidence: 94%

On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces

2016

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In the framework of complete probabilistic Menger metric spaces, this paper investigates some relevant properties of convergence of sequences built through sequences of operators which are either uniformly convergent to a strict k-contractive operator, for some real constant k ∈ (0, 1), or which are strictly k-contractive and point-wisely convergent to a limit operator. Those properties are also reformulated for the case when either the sequence of operators or its limit are strict -contractions. The definitions of strict (k and ) contractions are given in the context of probabilistic metric spaces, namely in particular, for the considered probability density function. A numerical illustrative example is discussed.

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“…The following is an example of a demicontractive mapping which is not quasinonexpansive mapping, for more details, see Chidume et al, [24] and references therein.…”

Section: Vector Spacesmentioning

confidence: 99%

A Note on the Split Common Fixed Point Problem and its Variant Forms

Kılıçman

Mohammed

2018

Mathematical Analysis and Applications

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The split common fixed point problems has found its applications in various branches of mathematics both pure and applied. It provides us a unified structure to study a large number of nonlinear mappings. Our interest here is to apply these mappings and propose some iterative methods for solving the split common fixed point problems and its variant forms, and we prove the convergence results of these algorithms.As a special case of the split common fixed problems, we consider the split common fixed point equality problems for the class of finite family of quasinonexpansive mappings. Furthermore, we consider another problem namely split feasibility and fixed point equality problems and suggest some new iterative methods and prove their convergence results for the class of quasinonexpansive mappings.Finally, as a special case of the split feasibility and fixed point equality problems, we consider the split feasibility and fixed point problems and propose Ishikawa-type extra-gradients algorithms for solving these split feasibility and fixed point problems for the class of quasi-nonexpansive mappings in Hilbert spaces. In the end, we prove the convergence results of the proposed algorithms.Results proved in this chapter continue to hold for different type of problems, such as; convex feasibility problem, split feasibility problem and multipleset split feasibility problems.

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The multiple-sets split equality fixed point problem for countable families of multi-valued demi-contractive mappings

Cited by 14 publications

References 15 publications

Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings

Viscosity approximation methods for the multiple-set split equality common fixed-point problems of demicontractive mappings

On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces

A Note on the Split Common Fixed Point Problem and its Variant Forms

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