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Quasi-variational, minimax inequalities, and collectively fixed point results
Donal O'Regan,Naseer Shahzad,Ravi P. Agarwal 대한수학회 2005 대한수학회보 Vol.42 No.4
The paper presents new collectively fixed point theorems, minimax and quasi-variational inequalities for maps in the S-KKM class.
Fixed point theory in Fr´echet spaces for M¨onch inward and contractive Urysohn type operators
Donal O'Regan 영남수학회 2008 East Asian mathematical journal Vol.24 No.3
We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss M¨onch Kakutani and contractive type maps.
QUASI-VARIATIONAL AND MINIMAX INEQUALITIES AND COLLECTIVELY FIXED POINT RESULTS FOR S-KKM MAPS
O'REGAN DONAL,SHAHZAD NASEER,AGARWAL RAVI P. Korean Mathematical Society 2005 대한수학회보 Vol.42 No.4
The paper presents new collectively fixed point theorems, minimax and quasi-variational inequalities for maps in the S-KKM class.
O'Regan, Donal The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.3
We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss $M{\ddot{o}}nch$ Kakutani and contractive type maps.
LEFSCHETZ FIXED POINT THEORY FOR COMPACT ABSORBING CONTRACTIVE ADMISSIBLE MAPS
조열제,Donal O'Regan,Baoqiang Yan 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.1
New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Fréchet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence of Banach spaces.
INCLUSION AND INTERSECTION THEOREMS WITH APPLICATIONS IN EQUILIBRIUM THEORY IN G-CONVEX SPACES
Mircea Balaj,Donal O'Regan 대한수학회 2010 대한수학회지 Vol.47 No.5
In this paper we obtain a very general theorem of p-compatibility for three multivalued mappings, one of them from the class B. More exactly, we show that given a G-convex space Y , two topological spaces X and Z, a (binary) relation p on 2Z and three mappings P : X ( Z,-Q : Y - Z and T ∈ B(Y,X) satisfying a set of conditions we can find (x, y) ∈ X ×Y such that x ∈ T(y) and P(ex)½ Q(ey). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.
FIXED POINTS AND HOMOTOPY RESULTS FOR CIRIC-TYPE MULTIVALUED OPERATORS ON A SET WITH TWO METRICS
Tania Lazar,Donal O'Regan,Adrian Petrusel 대한수학회 2008 대한수학회보 Vol.45 No.1
The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed
INCLUSION AND INTERSECTION THEOREMS WITH APPLICATIONS IN EQUILIBRIUM THEORY IN G-CONVEX SPACES
Balaj, Mircea,O'Regan, Donal Korean Mathematical Society 2010 대한수학회지 Vol.47 No.5
In this paper we obtain a very general theorem of $\rho$-compatibility for three multivalued mappings, one of them from the class $\mathfrak{B}$. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation $\rho$ on $2^Z$ and three mappings P : X $\multimap$ Z, Q : Y $\multimap$ Z and $T\;{\in}\;\mathfrak{B}$(Y,X) satisfying a set of conditions we can find ($\widetilde{x},\;\widetilde{y}$) ${\in}$ $X\;{\times}\;Y$ such that $\widetilde{x}\;{\in}\;T(\widetilde{y})$ and $P(\widetilde{x}){\rho}\;Q(\widetilde{y})$. Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.
FIXED POINTS AND HOMOTOPY RESULTS FOR ĆIRIĆ-TYPE MULTIVALUED OPERATORS ON A SET WITH TWO METRICS
Lazar, Tania,O'Regan, Donal,Petrusel, Adrian Korean Mathematical Society 2008 대한수학회보 Vol.45 No.1
The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed.
A NOTE ON THE LEFSCHETZ FIXED POINT THEOREM FOR ADMISSIBLE SPACES
AGARWAL, RAVI P.,O'REGAN DONAL Korean Mathematical Society 2005 대한수학회보 Vol.42 No.2
The Lefschetz fixed point theorem is extended to compact continuous maps defined on an admissible subset of a Hausdorff topological space.