strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

fixed point iterations for asymptotically nonexpansive mappings in banach spaces in this paper we suggest and analyze a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces the new iterative scheme includes ishikawa type and mann type interations as special cases the results obtained in this paper represent an extension as well as refinement of previous known results

iterative construction of fixed points of asymptotically nonexpansive mappings abstract let t be a completely continuous and asymptotically nonexpansive self mapping of a nonempty closed bounded and convex subset of a hilbert space then under certain conditions the sequence defined by xn 1 ntn xn 1 n x n converges strongly to some fixed point of t a similar result is obtained for asymptotically pseudocontractive mappings whose iterates are lipschitz continuous with respect to some common lipschitz constant

lyapunov inequalities for partial differential equations abstract this paper is devoted to the study of l p lyapunov type inequalities 1 p for linear partial differential equations more precisely we treat the case of neumann boundary conditions on bounded and regular domains in r n it is proved that the relation between the quantities p and n 2 plays a crucial role this fact shows a deep difference with respect to the ordinary case the linear study is combined with schauder fixed point theorem to provide new conditions about the existence and uniqueness of solutions for resonant nonlinear problems

on the multivariate lyapunov inequalities abstract we transfer some known univariate lyapunov type inequalities to the multivariate setting of a shell via the polar method our results are better than some results of anastassiou 2011 6 for even order partial differential equations

a new three step fixed point iteration scheme for asymptotically nonexpansive mappings in the present paper we define and study a new three step iterative scheme inspired by suantai j math anal appl 311 2005 506 517 this scheme includes many well known iterations for examples modified mann type modified ishikawa type iterative schemes and the three step iterative scheme of xu and noor several convergence theorems of this scheme are established for asymptotically nonexpansive mappings our results extend and improve the recent ones announced by schu j math anal appl 158 1991 407 413 bull aust math soc 43 1991 153 159 xu and noor j math anal appl 267 2002 444 453 suantai j math anal appl 311 2005 506 517 and many others a misleading conclusion of theorem 2 6 in suantai s paper is also corrected

a modified topsis with a different ranking index abstract as a tool for decision analysis the topsis technique for order preference by similarity to ideal solution attempts to choose alternative that should simultaneously have the closest distance from the positive ideal solution pis and the farthest distance from the negative ideal solution nis although the ranking index of topsis is reasonable it contains a flaw that is this ranking index is irrespective of the weights of separations of an alternative from the pis and the nis in other words no matter what weights the decision maker assigns to these two separations the ranking results would not differ as if he has no preference for these two separations this flaw will certainly limit the applicability of topsis by treating the separations of an alternative from the pis and the nis as a cost criterion and a benefit criterion respectively we reduced the original mcdm multi criteria decision making problem to a new mcdm problem with these two criteria only by proposing w and w as the weights of the cost criterion and the benefit criterion respectively we defined a new ranking index experimental results showed that if the number of alternatives exceeds two or if the relative importance of the two separations should be considered the proposed ranking index would be a better choice finally two numerical examples of a real life case are given for illustration in summary the proposed ranking index is intelligible and intrinsically superior to the original ranking index in seeking compromised solutions

weak and strong convergence theorems for finite families of asymptotically nonexpansive mappings in banach spaces abstract let e be a real uniformly convex banach space whose dual space e satisfies the kadec klee property k be a closed convex nonempty subset of e let t 1 t 2 t m k k be asymptotically nonexpansive mappings of k into e with sequences respectively k i n n 1 satisfying k i n 1 as n i 1 2 m and n 1 k i n 1 for arbitrary 0 1 let i n n 1 be a sequence in 1 for each i 1 2 m respectively let x n be a sequence generated for m 2 by x 1 k x n 1 1 1 n x n 1 n t 1 n y n m 2 y n m 2 1 2 n x n 2 n t 2 n y n m 3 y n 1 m n x n m n t m n x n n 1 let i 1 m f t i then x n converges weakly to a common fixed point of the family t i i 1 m under some appropriate condition on the family t i i 1 m a strong convergence theorem is also proved

lyapunov inequality for an elliptic problem with the robin boundary condition in this paper we study the lq lyapunov type inequalities for quasi linear elliptic problems with the robin boundary conditions in which the principal part of the equation is p laplacian operator similar problems have been considered by several authors for linear elliptic problems with the dirichlet or neumann boundary conditions we show that the critical value of the problem is n 1 p 1 where n is the dimension of the domain we reveal the relation between this critical value and the critical exponent p of the trace sobolev embedding w1 p lp

convergence theorems for a countable family of lipschitzian mappings this paper is concerned with convergence of an approximating common fixed point sequence of countable lipschitzian mappings in a uniformly convex banach space we introduce a new condition for a class of mappings to obtain several weak and strong convergence theorems this new condition is implied by many previous known conditions introduced by many authors we also apply our results for a class of nonexpansive mappings and asymptotically nonexpansive mappings and we immediately obtain convergence theorems proved by song chen kimura takahashi tan xu and many others

lyapunov inequalities for the periodic boundary value problem at higher eigenvalues this paper is devoted to provide some new results on lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues our main result is derived from a detailed analysis on the number and distribution of zeros of nontrivial solutions and their first derivatives together with the study of some special minimization problems this allows to obtain the optimal constants our applications include the hill s equation where we give some new conditions on its stability properties and also the study of periodic and nonlinear problems at resonance where we show some new conditions which allow to prove the existence and uniqueness of solutions

a reconsideration on convergence of three step iterations for asymptotically nonexpansive mappings abstract we illustrate that the control conditions of the main convergence theorems of yao and noor convergence of three step iterations for asymptotically nonexpansive mappings appl math comput in press are incorrect we also provide new control conditions which are complementary to nilsrakoo and saejung s results w nilsrakoo s saejung a new three step fixed point iteration scheme for asymptotically nonexpansive mappings appl math comput 181 2006 1026 1034

weak and strong convergence criteria of noor iterations for asymptotically nonexpansive mappings in this paper weak and strong convergence theorems are established for a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces mann type and ishikawa type iterations are included by the new iterative scheme the results obtained in this paper extend and improve the recent ones announced by xu and noor glowinski and le tallec noor ishikawa and many others

an algorithmic method to extend topsis for decision making problems with interval data in this paper from among multi criteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity ideal solution topsis approach has been dealt with in some cases determining precisely the exact value of the attributes is difficult and that as a result of this their values are considered as intervals therefore the aim of this paper is to extend the topsis method for decision making problems with interval data by extension of topsis method an algorithm to determine the most preferable choice among all possible choices when data is interval is presented finally an example is shown to highlight the procedure of the proposed algorithm at the end of this paper 2005 elsevier inc all rights reserved

rim reference ideal method in multicriteria decision making abstract multiple criteria decision making methods provide a useful tool to support decision making to date different methods have been developed using different approaches in particular the conception used by the topsis and vikor methods identifies the best alternative based on the positive and the negative ideal solutions in this paper a new method based on the concept of ideal solution is presented as a possible variant of the aforementioned however in our case these values can vary between the maximum value and the minimum value this does not occur in the vikor and topsis methods in which these values are the extreme values moreover our method is characterized to be independent of the type of data moreover rim does not present rank reversal an aspect that is not present in other multiple criteria decision making methods

on modified iterative method for nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

strong convergence theorem for uniformly l lipschitzian asymptotically pseudocontractive mapping in real banach space abstract let e be a real banach space let k be a nonempty closed and convex subset of e t k k a uniformly l lipschitzian asymptotically pseudocontractive mapping with sequence k n n 0 1 lim n k n 1 such that f t let n n 0 0 1 be such that n 0 n n 0 n 2 and n 0 n k n 1 suppose x n n 0 is iteratively defined by x n 1 1 n x n n t n x n n 0 and suppose there exists a strictly increasing continuous function 0 0 0 0 such that t n x x j x x k n x x 2 x x x k it is proved that x n n 0 converges strongly to x f t it is also proved that the sequence of iteration x n defined by x n 1 a n x n b n t n x n c n u n n 0 where u n n 0 is a bounded sequence in k and a n n 0 b n n 0 c n n 0 are sequences in 0 1 satisfying appropriate conditions converges strongly to a fixed point of t

using the hamming distance to extend topsis in a fuzzy environment considering the fact that in some cases determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data this paper extends the topsis method for dealing with fuzzy data and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented in this approach to identify the fuzzy ideal solution and fuzzy negative ideal solution one of the yager indices which is used for ordering fuzzy quantities in 0 1 is applied using yager s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives then the hamming distance is proposed for calculating the distance between two triangular fuzzy numbers finally an application is given to clarify the main results developed in the paper

approximation of common fixed points of a countable family of nonexpansive mappings in a banach space in this paper to find a common fixed point of a family of nonexpansive mappings we introduce a halpern type iterative sequence then we prove that such a sequence converges strongly to a common fixed point of nonexpansive mappings moreover we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings and the problem of finding a zero of an accretive operator

minimization problem related to a lyapunov inequality abstract in this study we consider the following minimization problem on a bounded smooth domain in r n s inf u 2 2 u 2 2 u h 1 0 u 2 2 u 0 this minimization problem plays a crucial role in the study of l p lyapunov type inequalities 1 p for linear partial differential equations with neumann boundary conditions in this study we prove the existence of minimizers of s as a consequence we prove the l p lyapunov type inequality in the critical case which was left open in 4

weak and strong convergence theorems for countable lipschitzian mappings and its applications abstract we use mann s iteration and the hybrid method in mathematical programming to obtain weak and strong convergence to common fixed points of a countable family of lipschitzian mappings finally we apply our results to solve the equilibrium problems and variational inequalities for continuous monotone mappings

a lyapunov type inequality for a ψ laplacian operator abstract we prove a lyapunov type inequality for a laplacian operator where is an odd increasing function which is sub multiplicative on 0 and s 1 s is a convex function for s 0 from this inequality we easily derive some previous results on the number of zeros nodal domains and bounds on eigenvalues of nontrivial solutions for certain boundary value problems including the p laplacian our method of proof does not require the standard approach via classical jensen cauchy schwarz and holder inequalities

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

extensions of topsis for multi objective large scale nonlinear programming problems in this paper we focus on multi objective large scale nonlinear programming molsnlp problems with block angular structure we extend technique for order preference by similarity ideal solution topsis approach to solve molsnlp problems compromise topsis control minimizes the measure of distance providing that the closest solution should have the shortest distance from the positive ideal solution pis as well as the longest distance from the negative ideal solution nis as the measure of closeness l p metric is used thus we reduce a q dimensional objective space to a two dimensional space by a first order compromise procedure the concept of membership function of fuzzy set theory is used to represent the satisfaction level for both criteria also we get a single objective large scale nonlinear programming lsnlp problem using the max min operator for the second order compromise operation finally a numerical illustrative example is given to clarify the main results developed in the paper

extension of the topsis method for decision making problems with fuzzy data decision making problem is the process of finding the best option from all of the feasible alternatives in this paper from among multicriteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity to ideal solution topsis approach has been dealt with in real word situation because of incomplete or non obtainable information the data attributes are often not so deterministic there for they usually are fuzzy imprecise therefore the aim of this paper is to extend the topsis method to decision making problems with fuzzy data in this paper the rating of each alternative and the weight of each criterion are expressed in triangular fuzzy numbers the normalized fuzzy numbers is calculated by using the concept of a cuts finally a numerical experiment is used to illustrate the procedure of the proposed approach at the end of this paper

strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups abstract the mann iterations for nonexpansive mappings have in general only weak convergence in a hilbert space we modify an iterative method of mann s type introduced by nakajo and takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 for nonexpansive mappings and prove strong convergence of our modified mann s iteration processes for asymptotically nonexpansive mappings and semigroups

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

lyapunov type inequalities for partial differential equations in this work we present a lyapunov inequality for linear and quasilinear elliptic differential operators in n dimensional domains we also consider singular and degenerate elliptic problems with ap coefficients involving the p laplace operator with zero dirichlet boundary condition as an application of the inequalities obtained we derive lower bounds for the first eigenvalue of the p laplacian and compare them with the usual ones in the literature

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis