a certain class of starlike functions this paper presents a new class of functions analytic in the open unit disc and closely related to the class of starlike functions besides being an introduction to this field it provides an interesting connections defined class with well known classes the paper deals with several ideas and techniques used in geometric function theory the order of starlikeness in the class of convex functions of negative order is also considered here

fuzzy n cell numbers and the differential of fuzzy n cell number value mappings in this paper we give the definition of a special kind of n dimension fuzzy numbers fuzzy n cell numbers discuss their operations and representation theorems define a complete metric on the fuzzy n cell number space and prove that the metric is equivalent to the supremum metric derived by the hausdorff metric between the level sets of the n dimension fuzzy numbers and obtain an embedding theorem of the fuzzy n cell number space isometrically embeds it into a concrete banach space we also consider the differential of the fuzzy mappings from an interval into the fuzzy n cell number space by using the embedding theorem

linear programming with fuzzy variables in practice there are many problems in which all decision parameters are fuzzy numbers and such problems are usually solved by either possibilistic programming or multiobjective programming methods unfortunately all these methods have shortcomings in this note using the concept of comparison of fuzzy numbers we introduce a very effective method for solving these problems then we propose a new method for solving linear programming problems with fuzzy variables

the fekete szego problem for k uniformly convex functions and for a class defined by the owa srivastava operator abstract by making use of a fractional differential operator due to owa and srivastava a subclass of analytic functions related to k uniformly convex functions is introduced for this class and in particular for the class of k uniformly convex functions the fekete szego problem is completely solved

extrapolation and weighted norm inequalities between lebesgue and lipschitz spaces in the variable exponent context abstract we give extrapolation results starting from weighted inequalities between lebesgue and lipschitz spaces given by 0 1 sup b w b b 1 n b f x m b f d x c g w s where 1 0 1 n 1 1 s f and g are two measurable functions and w belongs to a suitable class of weights from this hypothesis we obtain a large class of inequalities including weighted l p l q estimates and weighted l p lipschitz integral spaces generalizing well known results for certain sublinear operator from the same hypothesis 0 1 we obtain the corresponding results in the setting of variable exponent spaces particularly we obtain estimates of the type l p variable versions of lipschitz integral spaces we also prove a surprising weighted inequalities of the type l p l q an important tool in order to get the main results is an improvement of an estimate due to calderon and scott in 1 which allows us to relate different integral lipschitz spaces our results are new even in the classical context of constant exponents

subordination results on harmonic k uniformly convex mappings and related classes the main purpose of this paper is to establish some connections between certain classes of harmonic univalent functions by applying a number of convolution properties involving hypergeometric functions to be more precise we investigate such connections with harmonic k uniformly convex and a related class k st mappings in the plane

a taxonomy and review of the fuzzy data envelopment analysis literature two decades in the making data envelopment analysis dea is a methodology for measuring the relative efficiencies of a set of decision making units dmus that use multiple inputs to produce multiple outputs crisp input and output data are fundamentally indispensable in conventional dea however the observed values of the input and output data in real world problems are sometimes imprecise or vague many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in dea in this study we provide a taxonomy and review of the fuzzy dea methods we present a classification scheme with four primary categories namely the tolerance approach the a level based approach the fuzzy ranking approach and the possibility approach we discuss each classification scheme and group the fuzzy dea papers published in the literature over the past 20 years to the best of our knowledge this paper appears to be the only review and complete source of references on fuzzy dea

solving fuzzy stochastic linear programming problems using superiority and inferiority measures in this paper the author presents a model to measure the superiority and inferiority of fuzzy numbers fuzzy stochastic variables then the new measures are used to convert the fuzzy stochastic linear program into the corresponding deterministic linear program numerical examples are provided to illustrate the effectiveness of the proposed method

generalized fuzzy linear programming for decision making under uncertainty feasibility of fuzzy solutions and solving approach in this study a generalized fuzzy linear programming gflp method is developed for dealing with uncertainties expressed as fuzzy sets the feasibility of fuzzy solutions of the gflp problem is investigated a stepwise interactive algorithm sia based on the idea of design of experiment is then advanced to solve the gflp problem this sia method was implemented through i discretizing membership grade of fuzzy parameters into a finite number of a cut levels ii converting the gflp model into an interval linear programming ilp submodel under every a cut level iii solving the ilp submodels through an interactive algorithm and obtaining the associated interval solutions iv acquiring the membership functions of fuzzy solutions through statistical regression methods a simple numerical example is then proposed to illustrate the solution process of the gflp model through sia a comparison between the solutions obtained though sia and monte carlo method is finally conducted to demonstrate the robustness of the sia method the results indicate that the membership functions for decision variables and objective function are reasonable and robust

duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables linear programming problems with trapezoidal fuzzy variables fvlp have recently attracted some interest some methods have been developed for solving these problems by introducing and solving certain auxiliary problems here we apply a linear ranking function to order trapezoidal fuzzy numbers then we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results in particular we prove that the auxiliary problem is indeed the dual of the fvlp problem having established the dual problem the results will then follow as natural extensions of duality results for linear programming problems with crisp data finally using the results we develop a new dual algorithm for solving the fvlp problem directly making use of the primal simplex tableau this algorithm will be useful for sensitivity or post optimality analysis when using primal simplex tableaus

on a generalization of uniformly convex and related functions in this paper we define and study some subclasses of analytic functions by using the concept of k uniformly convexity several interesting properties coefficients and radius problems are investigated the behaviour of these classes under a certain integral operator is also studied we indicate the relevant connections of our results with various known ones

remarks on functional canonical variates alternating least squares methods and ace we discuss properties of some data analytic methods which are intimately related to each other alternating least squares als correspondence analysis and more recently breiman and friedman s ace algorithm the application of these methods to regression produces nonparametric estimators of nonlinear transformations both of the response and the predictors we point out some anomalies as well as some curiosities in the mathematics of these methods and we relate them to some areas in computer aided tomography projection pursuit regression and nonlinear devices in the theory of noise

duality in fuzzy number linear programming by use of a certain linear ranking function we explore some duality properties in fuzzy number linear programming problems by use of a linear ranking function we introduce the dual of fuzzy number linear programming primal problems we then present several duality results

some subclasses of close to convex mappings associated with conic regions in this paper we introduce and investigate several new subclasses of close to convex functions and their related mappings various interesting properties including sufficiency criteria coefficient estimates arc length problem and radius of convexity are investigated

an integrated decision support approach for project investors in risky and uncertain environments in project investment decisions it is often assumed that estimated values of project parameters are certain and they would not deviate by the time however project parameters normally change during a life cycle of the project therefore an existence of a deviation or gap between forecasted values and actual values is inevitable because of the uncertainty of the future forecasting the true and exact values of project parameters is almost impossible in this study an integrated decision support approach based on simulation and fuzzy set theory is proposed for project investors in risky and uncertain environments this approach determines the risk levels of the projects and helps investors to make investment decisions in the scope of the study a flowchart is presented to guide to decision maker in different situations of information uncertainty that belongs to project parameter values via this flowchart the values of project parameters can be chosen depending on how they are determined deterministic stochastic or fuzzy by project analyst besides calculating and analyzing the project risk in all possible situations would be easier illustrative examples are given to demonstrate the application of this approach

solving linear programming problems under fuzziness and randomness environment using attainment values in this paper the author presents a model to measure attainment values of fuzzy numbers fuzzy stochastic variables these new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem numerical comparisons are provided to illustrate the effectiveness of the proposed method

riesz transforms related to schrodinger operators acting on bmo type spaces abstract in this work we obtain boundedness on suitable weighted bmo type spaces of riesz transforms and their adjoints associated to the schrodinger operator v where v satisfies a reverse holder inequality our results are new even in the unweighted case

the fekete szego problem for subclasses of analytic functions defined by a differential operator related to conic domains by using a linear multiplier fractional differential operator a new subclass of analytic functions generalized b uniformly convex functions denoted by b sp l m n a c is introduced for this class the fekete szego problem is completely solved various known or new special cases of our results are also pointed out

the efficiency of investment information we investigate how the description of a correlated information v improves the investment in the stock market x the objective is to maximize the growth rate of wealth in repeated investments we find a single letter characterization of the incremental growth rate spl delta r the maximum increase in growth rate when v is described to the investor at rate r the incremental growth rate specialized to the horse race market is related to source coding with side information of wyner and ahlswede kormer we provide two horse race examples jointly binary and jointly gaussian the initial efficiency spl delta 0 is the maximum possible increase in the growth rate per bit of description we show that the initial efficiency is related to the dependency between v and the market in particular for the horse race market the initial efficiency is the square of the hirschfeld gebelein renyi maximal correlation between v and x this provides a connection with the hypercontraction of the markov operator of ahlswede and gacs for the general market the initial efficiency is 1 when the side information v is equal to the stock market outcome x

hypergeometric functions in the geometric function theory abstract in this lecture uses and influences of hypergeometric functions both kummer s and confluent hypergeometric functions in the study of geometric function theory and its generalizations are discussed as a survey of the author s work

on coefficient inequalities of functions associated with conic domains in this paper the concepts of janowski functions and the conic regions are combined to define a new domain which represents the conic type regions different views of this modified conic domain for specific values are shown graphically for better understanding of the behavior of this domain the class of such functions which map the open unit disk e onto this modified conic domain is defined also the classes of k uniformly janowski convex and k janowski starlike functions are defined and their coefficient inequalities are formulated the coefficient bound for a certain class of analytic functions proved by owa et al 2006 in 16 has also been improved

some extremal bounds for subclasses of univalent functions in this paper we obtain the sharp lower bound for ref z z u for functions f that are k uniformly convex in the unit disk u next we consider the problem of finding the minimum of ref z for functions f that are k uniformly convex in the disk of radius r corresponding results for the class of starlike functions related to the class of k uniformly convex functions are presented

a coefficient inequality for a subclass of the caratheodory functions defined using conical domains for 0 k k 2 u 1 2 v 2 u 0 let q k z be the riemann map of u z c z 0 let p q k be the class of analytic functions h z subordinate in u to q k z and represented by h z 1 b 1z b 2z 2 z u sharp estimates for b 2 ub 1 2

on classes of analytic functions related to conic domains abstract we introduce classes of analytic functions related to conic domains using a new linear multiplier fractional differential operator d n n n 0 0 1 0 1 0 which is defined as d 0 f z f z d 1 f z 1 f z z f z d f z d 2 f z d d 1 f z d n f z d d n 1 f z where f z 2 z d z f z and d z is the known fractional derivative basic properties of these classes are studied such as inclusion relations and coefficient bounds various known or new special cases of our results are also pointed out

generalized hypergeometric functions associated with k uniformly convex functions abstract for a certain linear operator which is defined by means of the hadamard product or convolution with a generalized hypergeometric function the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as for example k uniformly convex functions and k starlike functions relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out

some radius results for univalent functions abstract this paper deals with the geometrically motivated properties uniform starlikeness uniform convexity and starlikeness with respect to symmetrical points we give sharp radius results for these properties in the class s of normalized univalent functions corresponding results in the class s of starlike functions are also discussed

lipschitz type smoothness of the fractional integral on variable exponent spaces fil ramseyer mauricio javier consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet santa fe instituto de matematica aplicada del litoral universidad nacional del litoral instituto de matematica aplicada del litoral argentina

measure of efficiency in dea with fuzzy input output levels a methodology for assessing ranking and imposing of weights restrictions in this paper a fuzzy comparison of fuzzy numbers is defined and a slack based measure sbm model in data envelopment analysis dea is extended to be a fuzzy dea model using it proposed measure is employed for evaluation and ranking of all decision making units using a fuzzy concept called fuzzy profit also it is shown that the introduced model is convenient for using weights restrictions furthermore we compare the results of proposed model with guo and tanaka s results fuzzy sets syst 119 2001 149 by representing a numerical example introduced by them

measuring the satisfaction of constraints in fuzzy linear programming the paper proposes a new kind of method for solving fuzzy linear programming problems based on the satisfaction or fulfillment degree of the constraints using a new ranking method of fuzzy numbers the fulfillment of the constraints can be measured then the properties of the ranking index are discussed with this ranking index the decision maker can make the constraints tight or loose based on his optimistic or pessimistic attitude and get the optimal solution from the fuzzy constraint space the corresponding value of objective distribution function can be obtained a numerical example illustrates the merits of the approach

conic regions and k uniform convexity abstract let k c denote a domain such that 1 k and k is a conic section with eccentricity equal to 1 k in this paper authors introduce the class of k uniformly convex functions k ucv with the property that the values of the expression 1 zf z f z lie inside the domain k necessary and sufficient conditions for membership in k ucv as well as sharp growth and distortion theorems for k uniformly convex functions are given the obtained results generalize the concept of uniform convexity due to a w goodman ann polon math 56 1991 87 92

applications of certain operators to the classes of analytic functions related with generalized conic domains let a be the class of functions f f z z n 2 a nz n which are analytic in the open unit disc e we use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of a which map e onto a generalized form of the conic domain several properties of these classes including some inclusion relations convolution and other class preserving operators are studied in particular we derive many known and new results as special cases applications of some results are also given

weighted inequalities for negative powers of schrodinger operators abstract in this article we obtain boundedness of the operator v 2 from l p w into weighted bounded mean oscillation type spaces bmo l w under appropriate conditions on the weight w we also show that these weighted spaces also have a point wise description for 0 1 finally we study the behaviour of the operator v 2 when acting on bmo l w

radius problems in the class sl let sl denote the class of all analytic functions f in the unit disc u with the normalization f 0 f 0 1 0 and satisfying the conditionzf z f z 2 1 1 z u thus zf z f z is in the interior of the right half of the lemniscate of bernoulli x 2 y 2 2 2 x 2 y 2 0 the relations between sl and others classes geometrically defined are considered the radii of a convexity of a starlikeness and some of others of f sl are determined

on certain problem in the class of k starlike functions in this paper we consider the classes of k uniformly convex and k starlike functions defined in kanas and wisniowska 1999 2000 1 2 which generalize the class of uniformly convex functions introduced by goodman 1991 3 we discuss the real part of f z z when f is k starlike we find the minimum of ref z z improving the results obtained recently in wisniowska wajnryb 2009 11

on k uniformly close to convex functions of complex order in this paper we define and study some subclasses of analytic functions by using fractional derivative operator some interesting properties coefficients problems and inclusion results of these classes are investigated it is also shown that these classes are closed under convolution with convex functions and some applications are given

tabu search for fuzzy optimization and applications in this paper we present a tabu search technique to approximately solve fuzzy optimization problems we demonstrate the performance of the proposed method by applying it to an elementary fuzzy optimization problem other applications of the method to fuzzy linear programming fuzzy regression and the training of fuzzy neural networks are also presented

on a new class of analytic functions associated with conic domain abstract the aim of this paper is to generalize the conic domain defined by kanas and wisniowska and define the class of functions which map the open unit disk e onto this generalized conic domain a brief comparison between these conic domains is the main motivation of this paper a correction is made in selecting the range interval of order of conic domain

study on fuzzy optimization methods based on quasi linear fuzzy number and genetic algorithm fuzzy optimization is a well known optimization problem in artificial intelligence system control manufacturing and management establishing general and operable fuzzy optimization methods are important in both theory and application in this paper starting from the structure of fuzzy information and the mechanism of fuzzy optimization we propose the concept of quasi linear fuzzy number and discuss its approximation properties and the features on arithmetic operations further by distinguishing principal indices and secondary indices we establish the fuzzy optimization model based on synthesizing effect by combining the compound quantification strategy of fuzzy information and give a fuzzy optimization method based on principal operations and genetic algorithm fom bpo ga finally we consider the convergence of our algorithm using the theory of markov chains and analyze its performance through two concrete examples all these indicate that fom bpo ga can effectively merge decision preferences into the optimization process and it also possess better global convergence so it can be applied to many fuzzy optimization problems

subordination results for classes of analytic functions related to conic domains defined by a fractional operator abstract let a fractional operator d n n n 0 0 1 2 0 1 0 be defined by d 0 0 f z d 1 f z 1 f z z f z d f z d 2 f z d d 1 f z d n f z d d n 1 f z where f z 2 z d z f z and d z is the known fractional derivative in this paper several interesting subordination results are derived for certain classes of analytic functions related to conic domains defined by the operator d n which yield sharp distortion rotation theorems and koebe domain these results extended corresponding previously known results

characterization of optimal solutions of uncertainty investment problem in this paper we characterize the optimal profit best return of an investment problem with trapezoidal fuzzy numbers we give a solution algorithm to determine the optimal profit for investing of f money in the n investment polices alternative approach is considered for people who need to be more precise in their requirements illustrative example to determine the optimal profits of such problem is presented

classes of multivalent functions associated with a convolution operator we investigate several properties of the linear aouf silverman srivastava operator and associated classes of multivalent analytic functions which were introduced and studied by aouf et al m k aouf h silverman h m srivastava some families of linear operators associated with certain subclasses of multivalent functions comp math appl 55 2008 535 549 several theorems are extensions of earlier results of the above paper

certain sufficient conditions for a subclass of analytic functions involving hohlov operator making use of the hohlov operator the authors obtain inclusion relations between the classes of certain normalized analytic functions relevant connections of our work with the earlier works are pointed out

computational and theoretical pitfalls in some current performance measurement techniques and a new approach this paper addresses some pitfalls of some fuzzy data envelopment analysis models which have been provided in recent published papers this study deals with these papers from both computational and theoretical points of view moreover a new approach to deal with fuzzy data in dea framework is provided which does not have the mentioned pitfalls

study on fuzzy optimization methods based on principal operation and inequity degree fuzzy optimization is a well known optimization problem in artificial intelligence manufacturing and management so establishing general and operable fuzzy optimization methods are important in both theory and application in this paper by distinguishing principal indices and secondary indices we give a method for comparing fuzzy information based on synthesizing effect and an operation for achieving fuzzy optimization based on a principal indices transformation further we propose an axiomatic system for fuzzy inequity degree based on the essence of constraint and give an instructive metric method for fuzzy inequity degree then by combining with genetic algorithm we give some fuzzy optimization methods based on principal operation and inequity degree denoted by bpo id fga for short finally we consider the convergence of our algorithm using the theory of markov chains and analyze its performance through two concrete examples all these indicate that bpo id fga can effectively merge decision preferences into the optimization process and that it also possesses better global convergence so it can be applied to many fuzzy optimization problems

sobolev bmo and fractional integrals on super critical ranges of lebesgue spaces abstract in this article we explore the mapping and boundedness properties of linear and bilinear fractional integral operators acting on lebesgue spaces with large indices the prototype order fractional integral operator is the riesz potential i and the standard estimates for i are from l p into l q when 1 p n and 1 p 1 q n we show that a order linear fractional integral operator can be continuously extended to a bounded operator from l p into the sobolev bmo space i s b m o when n p and 0 s satisfy 1 p s n likewise we prove estimates for order bilinear fractional integral operators from l p 1 l p 2 into i s b m o for various ranges of the indices p 1 p 2 and s satisfying 1 p 1 1 p 2 s n

boundedness of the fractional integral on weighted lebesgue and lipschitz spaces necessary and sufficient conditions are given for the fractional integral operator 1i to be bounded from weighted strong and weak lp spaces within the range p n a into suitable weighted bmo and lipschitz spaces we also characterize the weights for which 1i can be extended to a bounded operator from weighted bmo into a weighted lipschitz space of order o finally under an additional assumption on the weight we obtain necessary and sufficient conditions for the boundedness of i between weighted lipschitz spaces 0 introduction a nonnegative function w defined on tn is called a weight if it is locally integrable we denote by jel the lebesgue measure of e and w e few x dx given a ball b gb will mean the ball with the same center as b and with radius 0 times as long throughout this paper the letter c will denote a constant not necessarily the same at each occurrence a weight w is said to belong to the muckenhoupt class ap 1 p oo if there exists a constant c such that w b i1 b p 1 rbi ibi for every ball b c r the class a1 is defined replacing the above inequality by 1w 1xb11 w b 0c 1 o ibi where xb is the characteristic function of the ball b we shall say that a weight w satisfies a doubling condition if there exists a constant c such that w 2b cw b received by the editors june 26 1995 1991 mathematics subject classification primary 42b25

on α convex functions related to shell like functions connected with fibonacci numbers abstract this paper presents a new class slm of functions f z analytic and normalized in the open unit disc u z z 1 which is related to a shell like curve and associated with fibonacci numbers satisfying the condition that 1 zf z f z 1 zf z f z p u z u where is a real number and p z z 2 z 2 1 z 2 z 2 1 5 2 z u the class slm being closely related to the classes of starlike and convex functions we apply some basic techniques to investigate certain interesting properties given below for this class of functions some important observations of the main results are also mentioned

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