scholarly journals Fixed Point Theorems for Asymptotically Contractive Multimappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
M. Djedidi ◽  
K. Nachi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Reflexive Banach Space ◽  
Existence Results ◽  
Coincidence Points ◽  
Set Valued Mapping ◽  
Asymptotic Contraction

We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.

scholarly journals The Bregman–Opial Property and Bregman Generalized Hybrid Maps of Reflexive Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1022
Author(s):  
Eskandar Naraghirad ◽  
Luoyi Shi ◽  
Ngai-Ching Wong
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Hilbert Spaces ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Reflexive Banach Space ◽  
Reflexive Banach Spaces ◽  
Opial Property ◽  
Expansive Maps ◽  
General Banach Space

The Opial property of Hilbert spaces is essential in many fixed point theorems of non-expansive maps. While the Opial property does not hold in every Banach space, the Bregman–Opial property does. This suggests to study fixed point theorems for various Bregman non-expansive like maps in the general Banach space setting. In this paper, after introducing the notion of Bregman generalized hybrid sequences in a reflexive Banach space, we prove (with using the Bregman–Opial property instead of the Opial property) convergence theorems for such sequences. We also provide new fixed point theorems for Bregman generalized hybrid maps defined on an arbitrary but not necessarily convex subset of a reflexive Banach space. We end this paper with a brief discussion of the existence of Bregman absolute fixed points of such maps.

Fixed point theorems for uniformly generalized Kannan type semigroup of self-mappings

2017 ◽  
Vol 26 (2) ◽  
pp. 231-240
Author(s):  
AHMED H. SOLIMAN ◽  
MOHAMMAD IMDAD ◽  
MD AHMADULLAH
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Real Banach Space ◽  
Normal Structure ◽  
Uniform Normal Structure

In this paper, we consider a new uniformly generalized Kannan type semigroup of self-mappings defined on a closed convex subset of a real Banach space equipped with uniform normal structure and employ the same to show that such semigroup of self-mappings admits a common fixed point provided the underlying semigroup of self-mappings has a bounded orbit.

scholarly journals A Class of Fractionalp-Laplacian Integrodifferential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yiliang Liu ◽  
Liang Lu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Laplacian Operator ◽  
Laplacian Equations

We study a class of nonlinear fractional integrodifferential equations withp-Laplacian operator in Banach space. Some new existence results are obtained via fixed point theorems for nonlocal boundary value problems of fractionalp-Laplacian equations. An illustrative example is also discussed.

Existence of solutions for Riemann–Liouville multi-valued fractional boundary value problems

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we study a class of Riemann–Liouville fractional differential inclusions with fractional boundary conditions. By using standard fixed point theorems, we obtain some new existence results for convex as well as nonconvex multi-valued mappings in an appropriate Banach space. The obtained results are illustrated by examples.

scholarly journals Fixed-point theorems for multivalued non-expansive mappings without uniform convexity

2003 ◽  
Vol 2003 (6) ◽  
pp. 375-386 ◽  
Author(s):  
T. Domínguez Benavides ◽  
P. Lorenzo Ramírez
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Fixed Point Theorems ◽  
Compact Convex ◽  
Contractive Mapping ◽  
Uniform Convexity ◽  
Opial Condition ◽  
The Family

LetXbe a Banach space whose characteristic of noncompact convexity is less than1and satisfies the nonstrict Opial condition. LetCbe a bounded closed convex subset ofX,KC(C)the family of all compact convex subsets ofC, andTa nonexpansive mapping fromCintoKC(C). We prove thatThas a fixed point. The nonstrict Opial condition can be removed if, in addition,Tis a1-χ-contractive mapping.

scholarly journals Coincidence points in θ - metric spaceS

2021 ◽  
Vol 20 ◽  
pp. 50-55
Author(s):  
Maha Mousa ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coincidence Points ◽  
Set Valued Mapping

In this paper, inspired by the concept of metric space, two fixed point theorems for α−set-valued mapping T:₳ → CB(₳), h θ (Tp,Tq) ≤ α(dθ(p,q)) dθ(p,q), where α: (0,∞) → (0, 1] such that α(r) < 1, ∀ t ∈ [0,∞) ) are given in complete θ −metric and then extended for two mappings with R-weakly commuting property to obtain a common coincidence point.

scholarly journals New results on Caputo fractional-order neutral differential inclusions without compactness

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
C. Ravichandran ◽  
Thabet Abdeljawad ◽  
N. Valliammal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Order ◽  
Weak Topology ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Neutral System

AbstractThis article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

scholarly journals On a fixed point theorem of Greguš

1986 ◽  
Vol 9 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Brian Fisher ◽  
Salvatore Sessa
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Convex Subset ◽  
Unique Common Fixed Point

We consider two selfmapsTandIof a closed convex subsetCof a Banach spaceXwhich are weakly commuting inX, i.e.‖TIx−ITx‖≤‖Ix−Tx‖   for   any   x   in   X,and satisfy the inequality‖Tx−Ty‖≤a‖Ix−Iy‖+(1−a)max{‖Tx−Ix‖,‖Ty−Iy‖}for allx,yinC, where0<a<1. It is proved that ifIis linear and non-expansive inCand such thatICcontainsTC, thenTandIhave a unique common fixed point inC.

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