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Agarwal, Ravi P.,Verma, Ram U. The Youngnam Mathematical Society Korea 2011 East Asian mathematical journal Vol.27 No.5
Based on the A-maximal(m)-relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong convergence results on proximal point algorithms in real Hilbert space settings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of variational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to first- order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for finding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.
FIXED POINT THEORY FOR MAPS HAVING CONVEXLY TOTALLY BOUNDED RANGES
Agarwal, Ravi-P.,O'regan, Donal Korean Mathematical Society 2001 대한수학회보 Vol.38 No.4
Three new fixed point theorems are presented for the set valued maps of Idzik. Moreover a continuation theorem for such maps is also given.
FIXED POINT THEORY FOR VARIOUS CLASSES OF PERMISSIBLE MAPS VIA INDEX THEORY
Agarwal, Ravi P.,O'Regan, Donal Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2
In this paper we use degree and index theory to present new applicable fixed point theory for permissible maps.
RANDOM FIXED POINT THEOREMS AND LERAY-SCHAUDER ALTERNATIVES FOR U<sub>c</sub><sup>k</sup> MAPS
AGARWAL RAVI P.,REGAN DONAL O Korean Mathematical Society 2005 대한수학회논문집 Vol.20 No.2
This paper presents new random fixed point theorems for $U_c^k$ maps and new random Leray-Schauder alternatives for $U_c^k$ type maps. Our arguments rely on recent deterministic fixed point theorems and on a result on hemicompact maps in the literature.
Boundary Value Problems for differential Inclusions with Fractional Order
Ravi P. Agarwal,Mouffak Benchohra,Samira Hamani 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.2
In this paper, we shall establish sucient conditions for the existence of so-lutions for a class of boundary value problem for fractional dierential inclusionsinvolving the Caputo fractional derivative. The both cases of convex and non-convex valued right hand sides are considered.
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.
Oscillation criteria for second order differential inclusions
Ravi P. Agarwal,Said R. Grace,Donal O`Regan 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.1
Some new criteria for the oscillation of second order dierential inclusion(a(t)y.(t)). ∈ F(t,y(t)) for a.e.t≥t0 ≥0 are established.
On solutions of a generalized neutral logistic differential equation
Ravi P. Agarwal,J´ozef Bana´s,Reza Mollapourasl,T. Gnana Bhaskar 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.2
We study a generalized neutral logistic differential equation with deviating argument. Using the classical Banach contraction principle on an equivalent nonlinear functional integral equation we establish the existence of a unique solution in a certain function space. A few examples along with a numerical solutions are presented.