scholarly journals Fixed points of a certain class of mappings in spaces with uniformly normal structure

1998 ◽  
Vol 21 (4) ◽  
pp. 677-680
Author(s):  
Jong Soo Jung ◽  
Balwant Singh Thakur ◽  
Daya Ram Sahu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Normal Structure ◽  
Regular Mapping ◽  
Asymptotically Regular

A fixed point theorem is proved in a Banach spaceEwhich has uniformly normal structure for asymptotically regular mappingTsatisfying: for eachx,yin the domain and forn=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖),wherean,bn,cnare nonnegative constants satisfying certain conditions. This result generalizes a fixed point theorem of Górnicki [1].

A Fixed Point Theorem for Semigroups of Proximately Uniformly Lipschitzian Mappings

1991 ◽  
Vol 34 (4) ◽  
pp. 559-562
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence Theorem ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Nonexpansive Semigroups ◽  
Lipschitzian Mappings ◽  
Lipschitzian Semigroup

AbstractAs a generalization of Kiang and Tan's proximately nonexpansive semigroups, the notion of a proximately uniformly Lipschitzian semigroup is introduced and an existence theorem of common fixed points for such a semigroup is proved in a Banach space whose characteristic of convexity is less than one.

Fixed Points for Dissipative-Repulsive Systems and Topological Dynamics of Mappings Defined on N-dimensional Cells

2005 ◽  
Vol 5 (3) ◽  
Author(s):  
Marina Pireddu ◽  
Fabio Zanolin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Topological Dynamics ◽  
Continuous Mappings ◽  
Expansion Condition ◽  
Dimensional Cell

AbstractWe prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of ℝ

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.

scholarly journals FIXED POINTS FOR TWO PAIRS OF ABSORBING MAPPINGS IN WEAK PARTIAL METRIC SPACES

2020 ◽  
pp. 283
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces

In this paper, a general fixed point theorem for two pairs of absorbing mappings in weak partial metric space, using implicit relations, has been proved.

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

scholarly journals Compatible mappings and common fixed points(2)

1988 ◽  
Vol 11 (2) ◽  
pp. 285-288 ◽  
Author(s):  
Gerald Jungck
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Compatible Mappings ◽  
Common Fixed Point Theorem

A common fixed point theorem of S.L. and S.P. Singh is generalized by weakening commutativity hypotheses and by increasing the number of functions involved.

scholarly journals Compatible mappings and common fixed points “revisited”

1994 ◽  
Vol 17 (1) ◽  
pp. 37-40 ◽  
Author(s):  
Gerald Jungck
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Common Fixed Points ◽  
Contraction Principle ◽  
Compatible Mappings ◽  
Type Contraction

A fixed point theorem involving a Meir-Keeler type contraction principle is refined by diminishing continuity requirements.

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