In this article, we introduce a new approach to common fixed point theory for a weak compatible p... more In this article, we introduce a new approach to common fixed point theory for a weak compatible pair. We first introduce the concepts of R-pair and NR-pair and establish some new common fixed point theorems for a weak compatible pair in hyperconvex metric spaces and uniformly convex metric spaces. We shall also establish the well-known De Marr's theorem for a family of weak compatible pairs in a hyperconvex metric space [0,1] and show by an example that it fails to hold in general hyperconvex metric spaces. Mathematics Subject Classification : Primary 06F30, 46B20, 47E10.
ABSTRACT. A collection,of,fixed,point,theorems,is generalized,by,replacing,hypothesized commutati... more ABSTRACT. A collection,of,fixed,point,theorems,is generalized,by,replacing,hypothesized commutativity,or weak,commutativity,of functions,involved,by compatibility. KEY WORDS AND PHRASES. F, weakly commuting mappings,
Fixed Point Theorems for Occasionally Weakly Compatible Mappings
We obtain two fixed point theorems for a class of operators called occasionally weakly compatible... more We obtain two fixed point theorems for a class of operators called occasionally weakly compatible maps defined on a symmetric space . These results establish two of the most general fixed point theorems for four maps.
It is proved that a planar continuum is nonseparating if and only if it is H-connected. A fixed-p... more It is proved that a planar continuum is nonseparating if and only if it is H-connected. A fixed-point theorem for spaces that can be written in terms of sequences of H-connected continua follows as a consequence.
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
... Such acts were expected to provoke manifestations of divine anger in the form of severe illne... more ... Such acts were expected to provoke manifestations of divine anger in the form of severe illness, sudden death and/or other misfortunes vis-ited on either the slayer or some member of his immediate family. Acts of homicide ...
Remarks and results regarding weak compatibility and proper orbits
ABSTRACT Known fixed and common fixed point results involving weakly compatible maps and maps wit... more ABSTRACT Known fixed and common fixed point results involving weakly compatible maps and maps with proper orbits are presented. These theorems, stated for Hausdorff topological spaces, provide motivation and basis for two new fixed point theorems for semi-metric spaces.
Let p : X ~ Y be a proper surjective local homeomorphism from the Hausdorff space X to the connec... more Let p : X ~ Y be a proper surjective local homeomorphism from the Hausdorff space X to the connected first countable Hausdorff space Y. Then X is a finite disjoint union X = Xl U ... U X n with each X j connected and with p : X j ~ X a surjectiv~, proper, local homeomorphism.
IThe limit space of an inverse sequence of H-connected metric continua in which all bonding maps ... more IThe limit space of an inverse sequence of H-connected metric continua in which all bonding maps are open surjective maps is itself H -connected.
ABSTRACT A result in best approxmiation theory of the second author is generalized by using a fix... more ABSTRACT A result in best approxmiation theory of the second author is generalized by using a fixed point theorem of the first author [PAMS 103, no.3 (1988), 977-983]. A similar result is given in Banach spaces using Opial's condition.
Common fixed points for noncontinuous nonself maps on nonmetric spaces
ABSTRACT Common fixed-point theorems for sets of two to four noncontinuous maps of a subset D of ... more ABSTRACT Common fixed-point theorems for sets of two to four noncontinuous maps of a subset D of a semimetric space X into X are proven. The role of weakly biased and weakly compatible maps in securing common fixed points in highlighted.
We consider a variation of the concept of compatible maps introduced by Hicks and Saliga 1), and ... more We consider a variation of the concept of compatible maps introduced by Hicks and Saliga 1), and obtain generalizations ofresults by Hicks and Saliga and others.
In this article, we introduce a new approach to common fixed point theory for a weak compatible p... more In this article, we introduce a new approach to common fixed point theory for a weak compatible pair. We first introduce the concepts of R-pair and NR-pair and establish some new common fixed point theorems for a weak compatible pair in hyperconvex metric spaces and uniformly convex metric spaces. We shall also establish the well-known De Marr's theorem for a family of weak compatible pairs in a hyperconvex metric space [0,1] and show by an example that it fails to hold in general hyperconvex metric spaces. Mathematics Subject Classification : Primary 06F30, 46B20, 47E10.
ABSTRACT. A collection,of,fixed,point,theorems,is generalized,by,replacing,hypothesized commutati... more ABSTRACT. A collection,of,fixed,point,theorems,is generalized,by,replacing,hypothesized commutativity,or weak,commutativity,of functions,involved,by compatibility. KEY WORDS AND PHRASES. F, weakly commuting mappings,
Fixed Point Theorems for Occasionally Weakly Compatible Mappings
We obtain two fixed point theorems for a class of operators called occasionally weakly compatible... more We obtain two fixed point theorems for a class of operators called occasionally weakly compatible maps defined on a symmetric space . These results establish two of the most general fixed point theorems for four maps.
It is proved that a planar continuum is nonseparating if and only if it is H-connected. A fixed-p... more It is proved that a planar continuum is nonseparating if and only if it is H-connected. A fixed-point theorem for spaces that can be written in terms of sequences of H-connected continua follows as a consequence.
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
... Such acts were expected to provoke manifestations of divine anger in the form of severe illne... more ... Such acts were expected to provoke manifestations of divine anger in the form of severe illness, sudden death and/or other misfortunes vis-ited on either the slayer or some member of his immediate family. Acts of homicide ...
Remarks and results regarding weak compatibility and proper orbits
ABSTRACT Known fixed and common fixed point results involving weakly compatible maps and maps wit... more ABSTRACT Known fixed and common fixed point results involving weakly compatible maps and maps with proper orbits are presented. These theorems, stated for Hausdorff topological spaces, provide motivation and basis for two new fixed point theorems for semi-metric spaces.
Let p : X ~ Y be a proper surjective local homeomorphism from the Hausdorff space X to the connec... more Let p : X ~ Y be a proper surjective local homeomorphism from the Hausdorff space X to the connected first countable Hausdorff space Y. Then X is a finite disjoint union X = Xl U ... U X n with each X j connected and with p : X j ~ X a surjectiv~, proper, local homeomorphism.
IThe limit space of an inverse sequence of H-connected metric continua in which all bonding maps ... more IThe limit space of an inverse sequence of H-connected metric continua in which all bonding maps are open surjective maps is itself H -connected.
ABSTRACT A result in best approxmiation theory of the second author is generalized by using a fix... more ABSTRACT A result in best approxmiation theory of the second author is generalized by using a fixed point theorem of the first author [PAMS 103, no.3 (1988), 977-983]. A similar result is given in Banach spaces using Opial's condition.
Common fixed points for noncontinuous nonself maps on nonmetric spaces
ABSTRACT Common fixed-point theorems for sets of two to four noncontinuous maps of a subset D of ... more ABSTRACT Common fixed-point theorems for sets of two to four noncontinuous maps of a subset D of a semimetric space X into X are proven. The role of weakly biased and weakly compatible maps in securing common fixed points in highlighted.
We consider a variation of the concept of compatible maps introduced by Hicks and Saliga 1), and ... more We consider a variation of the concept of compatible maps introduced by Hicks and Saliga 1), and obtain generalizations ofresults by Hicks and Saliga and others.
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