Fixed point theory for multivalued generalized nonexpansive mappings

Garcia-Falset, Jesús; Llorens-Fuster, Enrique; Gálvez, Elena Moreno

doi:10.2298/aadm120712017g

Cited by 17 publications

(7 citation statements)

References 21 publications

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“…Finally, we prove that a sequence defined by a three-step iteration ∆-converges (even on some condition strongly converges) to a fixed point of these kind of mappings. Our results extend and improve some results in [23] and [13].…”

Section: Nonexpansive If D(t X T Y) D(x Y)supporting

confidence: 90%

“…This class properly contains Suzuki's (C)-type mappings as (1.1) and several of its generalizations such as (C λ )-type mappings as (1.2) and (E µ )-type mappings as (1.3) mentioned before. The set-valued case for (L)-type mappings were discussed in [13] and more results in [24]. Their results closely depend upon geometric characteristics of the Banach space under consideration.…”

Section: Nonexpansive If D(t X T Y) D(x Y)mentioning

confidence: 99%

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Fixed point theorems for (L)-type mappings in complete CAT(0) spaces

Zhou¹,

Cui²

2017

J. Nonlinear Sci. Appl.

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In this paper, fixed point properties for a class of more generalized nonexpansive mappings called (L)-type mappings are studied in geodesic spaces. Existence of fixed point theorem, demiclosed principle, common fixed point theorem of single-valued and set-valued are obtained in the third section. Moreover, in the last section, ∆-convergence and strong convergence theorems for (L)-type mappings are proved. Our results extend the fixed point results of Suzuki's results in

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Section: Nonexpansive If D(t X T Y) D(x Y)supporting

confidence: 90%

Section: Nonexpansive If D(t X T Y) D(x Y)mentioning

confidence: 99%

Fixed point theorems for (L)-type mappings in complete CAT(0) spaces

Zhou¹,

Cui²

2017

J. Nonlinear Sci. Appl.

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“…Throughout the paper, (X, ∥ · ∥) will be a Banach space and given C ⊆ X, P(C) denotes the class of non-empty subsets of C. Following [9], given C ∈ P(X) we put…”

Section: Introductionmentioning

confidence: 99%

“…Then, it is natural try to extend the known fixed points results for singlevalued mappings to the multivalued case. In fact, there are many works about this issue, see for instance [1,4,9,13,14,16,22,28,29,30] and references therein. As expected, some issues related with the Theory of Fixed Point for multivalued mappings still remain open, see for instance [6].…”

Section: Introductionmentioning

confidence: 99%

Computing fixed points of nonexpansive mappings by $\alpha$-dense curves

García¹

2017

Journal of Nonlinear Analysis and Application

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Given a multivalued nonexpansive mapping defined on a convex and compact set of a Banach space, with values in the class of convex and compact subsets of its domain, we present an iteration scheme which (under suitable conditions) converges to a fixed point of such mapping. This new iteration provides us another method to approximate the fixed points of a singlevalued nonexpansive mapping, defined on a compact and convex set into itself. Moreover, the conditions for the singlevalued case are less restrictive than for the multivalued case. Our main tool will be the so called α-dense curves, which will allow us to construct such iterations. Some numerical examples are provided to illustrate our results.

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“…Fixed points and fixed point iteration process for nonexpansive mappings have been studied extensively by many authors to solve nonlinear operator equations, as well as variational inequalities; see, for example, [23][24][25][26][27][28]. In the recent years, fixed point theory for multivalued mappings has been studied by many authors; see [29][30][31][32][33][34][35][36][37][38][39][40] and the references therein.…”

mentioning

confidence: 99%