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On the growth analysis of iterated entire functions
Ravi P. Agarwal,Sanjib Kumar Datta,Tanmay Biswas,Pulak Sahoo 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.1
In the paper we prove some results relating to the comparative growth properties of iterated entire functions using (p; q) -th order and (p; q)- th lower order.
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.
ON CONSTANT-SIGN SOLUTIONS OF A SYSTEM OF DISCRETE EQUATIONS
Agarwal, Ravi-P.,O'Regan, Donal,Wong, Patricia-J.Y. 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.1
We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.
FIXED POINT THEORY FOR MULTIMAPS IN EXTENSION TYPE SPACES
P. Agarwal, Ravi,O'ReganDonal,ParkSehie Korean Mathematical Society 2002 대한수학회지 Vol.39 No.4
New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.
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.
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.
Ravi P. Agarwal,Ram U. Verma 영남수학회 2011 East Asian mathematical journal Vol.27 No.5
Abstract. Based on the A-maximal (m)-relaxed monotonicity frame-works, the approximation solvability of a general class of variational in-clusion problems using the relaxed proximal point algorithm is explored,while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modied version of the relaxed proximal point al-gorithm, 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 con-vergence results on proximal point algorithms in real Hilbert space set-tings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of vari-ational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to rst-order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for nding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.
Pythagorean Theorem Before and After Pythagoras
Ravi P. Agarwal 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.3
Following the footpaths of Lakshmikantham, et. al. [15], and succeeding by Agarwal et. al. [3], in this article a sincere effort has been made to report the origin of the Pythagorean Theorem. Out of about 500 known different proofs of this theorem, we select five which have historical importance. We also discuss several generalizations of this theorem, and list some antique enduring problems. We genuinely hope students and teachers of mathematics will appreciate this article.