rate of convergence of baskakov bezier type operators for locally bounded functions abstract in this paper we introduce baskakov bezier operator b n which is an operator of probabilistic type we study the rate of convergence of the operator b n for locally bounded functions by using some inequalities and results of probability theory our estimate is essentially the best possible

on generalized convexity of fuzzy variables maps in this paper we investigate the convexity and quasiconvexity of fuzzy functions by use the interval analysis some properties of convex and quasiconvex fuzzy functions are introduced applications of fuzzy convexity and quasiconvexity to optimality are discussed

a class of convex fuzzy mappings based on the concept of ordering defined by goetschel and voxman fuzzy sets and systems 18 1996 31 in this paper we present the concepts of epigraph and convexity of the fuzzy mappings and describe characteristics of the convex fuzzy mappings and quasi convex fuzzy mappings then we discuss the properties of convex fuzzy optimizations

preinvexity and φ 1 convexity of fuzzy mappings through a linear ordering the preinvexity prequasiinvexity 1 convexity and 1 quasiconvexity of fuzzy mappings are defined based on a linear ordering on the set of fuzzy numbers characterizations for these fuzzy mappings are obtained the local global minimum properties of real valued preinvex functions and 1 convex functions are extended to preinvex fuzzy mappings and 1 convex fuzzy mappings respectively it is also proved that every strict local minimizer of a prequasiinvex fuzzy mapping is a strict global minimizer and that every strict local minimizer of a 1 quasiconvex fuzzy mapping is a strict global minimizer

convex fuzzy mapping and operations of convex fuzzy mappings convex and concave fuzzy mappings are considered in this paper based on the seminal work of nanda and kar on the definition of convex fuzzy mapping the operations of convex fuzzy mapping are established some of the important concepts such as positively homogeneous infimal convolution right scalar multiplication and convex hull are introduced and the corresponding theorems are demonstrated by using the parametric representation of fuzzy numbers

rate of convergence by chlodowsky taylor polynomials approximation on an unbounded interval is studied in this work by means of a newly defined two parameter polynomial operator based on chlodowsky polynomials the operator s properties including convergence rate are investigated using the weighted modulus of continuity an example is given to illustrate the effect of the parameters some basic results are presented

local unstable manifolds of periodic orbits in thin domains abstract we compare the dynamics of a system of damped wave equations on a thin domain with the dynamics of the limit system when the thickness of the thin domain goes to 0 more precisely under the assumption that the problem in the thin domain admits a periodic orbit e close to a hyperbolic periodic orbit 0 of the problem in the limit domain we show that e is also hyperbolic and that the local unstable manifold of the periodic orbit e is close to the local unstable manifold of 0

on integration of fuzzy mappings abstract in this paper we introduce the concept of an integral of a fuzzy mapping this generalises the integral introduced by matloka 10 and also extends riemann stieltjes integral over a closed interval to fuzzy mappings

the bezier variant of kantorovitch operators in the present paper we define generalized kantorovitch type operators for particular values our operators reduce to the well known szasz kantorovitch operators and baskakov kantorovitch operators we estimate the rate of convergence of the bezier variant of these generalized operators for bounded variation functions here we also remark that for a particular value c 0 the second central moment was not estimated correctly in 1 which leads to the major error in the main results of 1

an estimate on the convergence of mkz bezier operators the pointwise approximation properties of the mkz bezier operators m n a f x for a 1 have been studied in x m zeng rates of approximation of bounded variation functions by two generalized meyer konig zeller type operators comput math appl 39 2000 1 13 the aim of this paper is to study the pointwise approximation of the operators m n a f x for the other case 0 a 1 by means of some new estimate techniques and a result of guo and qi s guo q qi the moments for the meyer konig and zeller operators appl math lett 20 2007 719 722 we establish an estimate formula on the rate of convergence of the operators m n a f x for the case 0 a 1

approximation by modified srivastava gupta operators in the present paper we give a modified form of srivastava gupta operators which preserve the constant as well as linear functions we represent these operators as a special cases in terms of hypergeometric series we study some of the approximation properties and statistical approximation for these operators

invex and generalized convex fuzzy mappings in this paper we introduce the concepts of pseudo convexity invexity and pseudo invexity for fuzzy mappings of one variable based on the notion of differentiability proposed by goetschel and voxman 4 and investigate the relationship between convex fuzzy mappings preinvex fuzzy mappings and these classes of fuzzy mappings we shall prove that pseudo convex fuzzy mappings and invex fuzzy mappings are pseudo invex and that a differentiable convex resp preinvex fuzzy mapping is pseudo convex resp invex in addition sufficient optimality conditions are obtained for pseudo convex invex and pseudo invex fuzzy mappings

the generalization of bivariate mkz operators by multiple generating functions in the present paper we study approximation properties of multiple generating functions type bivariate meyer konig and zeller mkz operators with the help of volkov type theorem we compute the order of convergence of these operators by means of modulus of continuity and the elements of modified lipschitz class finally we give application to partial differential equations

some properties of weakly convex fuzzy mappings in this paper we introduce the concepts of weakly convex fuzzy sets weakly convex fuzzy mappings and weakly quasi convex fuzzy mappings and then give characterization theorems for these fuzzy sets and fuzzy mappings

rate of pointwise approximation for locally bounded functions by szasz operators abstract in this paper the asymptotic behavior of szasz operators for locally bounded functions f is studied at points x where f x and f x exist an asymptotic estimate of this type approximation is obtained by using some techniques and results of probability theory the estimate essentially is the best possible for continuous points of f

a note on generalized convexity for fuzzy mappings through a linear ordering in de campos ibanez and gonzalez munoz fuzzy sets syst 29 145 154 1989 6 goestschel and voxman fuzzy sets syst 18 31 43 1986 7 the authors considered a linear ordering on the space of fuzzy intervals for each fuzzy mapping fuzzy interval valued mapping f based on the aforementioned linear ordering they introduced a real valued function t f on the domain of the fuzzy mapping f recently chalco cano et al fuzzy sets syst 231 70 83 2013 4 have studied the relationship between the generalized hukuhara differentiability of a fuzzy mapping f g differentiability for short and the differentiability of t f and some properties of local global minima this paper studies such properties for fuzzy mappings using new concepts which generalize the existing ones

differentiability and convexity of fuzzy mappings abstract goetschel and voxman 1 have introduced the notion of a derivative for fuzzy mappings of one variable in a manner different from the usual one in this paper we define a differentiable fuzzy mapping of several variables in ways that parallel the definition proposed by goetschel and voxman 1 for a fuzzy mapping of one variable and then study some basic differentiability properties of fuzzy mappings from the standpoint of convex analysis

approximation of unbounded functions by a new sequence of linear positive operators in the present paper we introduce a new sequence of linear positive operators to study the simultaneous approximation of unbounded functions

an estimate on the convergence of baskakov bezier operators abstract in the present paper we estimate the rate of convergence on functions of bounded variation for the bezier variant of the baskakov operators b n f x here we have studied the rate of convergence of b n f x for the case 0 1

approximation properties of bernstein durrmeyer type operators abstract this paper deals with the approximation of continuous functions by sequences of some modified bernstein durrmeyer type operators that reproduce certain test functions the orders of approximation of the new versions turn to be at least as good as the one of the genuine bernstein durrmeyer operators moreover by extrapolating techniques recently applied to the classical bernstein operators we present a one parameter family of modified sequences of operators that reproduce certain polynomials and possess that popular genuine sequence as a limit case comparisons and some illustrative graphics are also presented

on properties of convex fuzzy mappings the objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by goetschel and voxman firstly a new kind of fuzzy mapping termed semistrictly convex fuzzy mapping is defined through this linear ordering note that semistrict convexity does not imply convexity and the interrelationships among convex strictly convex and semistrictly convex mappings are established under certain conditions furthermore this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity finally some further characteristic properties for semistrictly convex fuzzy mappings are derived

approximation by complex genuine durrmeyer type polynomials in compact disks abstract in this paper the order of simultaneous approximation and voronovskaja kind results with quantitative estimate for the complex genuine durrmeyer polynomials attached to analytic functions on compact disks are obtained in this way we put in evidence the overconvergence phenomenon for the genuine durrmeyer polynomials namely the extensions of the approximation properties with quantitative estimates from real intervals to compact disks in the complex plane

convexity of n dimensional fuzzy number valued functions and its applications the aim of this study is to generalize convexity from vector valued maps to n dimensional fuzzy number valued functions and to investigate some relations among the convexity and generalized convexity of n dimensional fuzzy number valued functions which are based on a new ordering of n dimensional fuzzy numbers proposed in this study furthermore some criteria are obtained for the convexity and generalized convexity under the conditions of lower and upper semicontinuity respectively finally we study the local global minimum properties of the convex fuzzy number valued functions

on characterizations of preinvex fuzzy mappings several characterizations about preinvex fuzzy mapping are obtained in this paper firstly an equivalent condition of preinvex fuzzy mapping is established under certain conditions furthermore the necessary and sufficient conditions for differentiable and twice differentiable preinvex fuzzy mapping are provided by using the given equivalent condition of preinvex fuzzy mapping finally a new proof of some known important conclusions is offered these results generalize and improve some known results

approximation properties of bezier summation integral type operators based on polya bernstein functions in this article we introduce the bezier variant of summation integral type operators having polya and bernstein basis functions we give a direct approximation theorem by means of the first order modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation

pseudolinear fuzzy mappings two classes of fuzzy mappings called pseudolinear and pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo convex and pseudo invex fuzzy mappings first some characterizations of pseudolinear and pseudolinear fuzzy mappings are obtained then characterizations of the solution sets of pseudolinear and pseudolinear fuzzy programs are derived

generalized convexity in fuzzy vector optimization through a linear ordering in this article we study efficiency and weakly efficiency in fuzzy vector optimization after formulating the problem we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized hukuhara differentiability pseudoinvexity i and pseudoinvexity ii we prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem we give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex i and ii moreover we present some examples to illustrate the results lastly we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models

convergence rate of a new bezier variant of chlodowsky operators to bounded variation functions in the present paper we estimate the rate of pointwise convergence of the bezier variant of chlodowsky operators c n a for functions defined on the interval extending infinity of bounded variation to prove our main result we have used some methods and techniques of probability theory

bounds for bernstein basis functions and meyer konig and zeller basis functions abstract in this paper the inequality estimates of bernstein basis functions and meyer konig and zeller basis functions are studied exact bounds for these two basis functions are obtained moreover some application results of the new estimates in estimating the rate of convergence of durrmeyer operators and meyer koning and zeller operators for functions of bounded variation are also given

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

on convex and concave fuzzy mappings abstract in this paper we introduce the concepts of convex subsets of f 0 the set of all fuzzy numbers and monotonic fuzzy mappings on r2 and show that a monotonic fuzzy mapping f on a convex set c r1 or r2 is quasi convex and quasi concave we establish two characterizations for convex fuzzy mappings and two characterizations for concave fuzzy mappings we also prove the least upper bound property

rate of approximation by a new sequence of linear positive operators abstract in the present paper we study the rate of pointwise approximation by a new sequence of linear positive operators for functions of bounded variation to prove the main result we have used some results of probability theory in the end we also introduce the bezier variant of these newly introduced sequences of linear positive operators

bifurcation and multiplicity results for periodic solutions of a damped wave equation in a thin domain we study the bifurcation problem for periodic solutions of a nonautonomous damped wave equation dened in a thin domain here the bifurcation parameter is represented by the thinness 0 of the considered domain this study has as starting point the existence result of periodic solutions already stated by the authors for this equation and it makes use of the condensivity properties of the associated poincare map and its linearization around these solutions we establish sucient conditions to guarantee that 0 is or not a bifurcation point and a related multiplicity result these results are in the spirit of those given by krasnosel skii and they are obtained by using the topological degree theory for k condensing operators c 2000 elsevier science b v all rights reserved

convex fuzzy mapping with differentiability and its application in fuzzy optimization abstract the concepts of differentiability convexity generalized convexity and minimization of a fuzzy mapping are known in the literature the purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using buckley feuring approach for fuzzy differentiation and derive karush kuhn tucker condition for the constrained fuzzy minimization problem

approximation by stancu chlodowsky polynomials in this paper we investigate convergence and approximation properties of a chlodowsky type generalization of stancu polynomials we called stancu chlodowsky polynomials the rates of convergence of this generalization are obtained by means of modulus of continuity and by using the k functional of peetre we also present and prove theorems on weighted approximation and the order of approximation of continuous functions by these operators on all positive semi axis

rates of approximation of bounded variation functions by two generalized meyer konig and zeller type operators abstract in this paper the approximation behaviours of two generalized meyer konig and zeller type operators m n and m n are studied by means of the decomposition technique of functions of bounded variation and the method of bojanic 1 bojanic and vuilleumier 2 and cheng 3 together with some results from probability theory and the exact bound of meyer konig and zeller operators basis functions the rates of convergence of these two operators for functions of bounded variation are obtained

certain new classes of durrmeyer type operators in the present paper we estimate the rate of convergence for functions having bounded derivatives for certain durrmeyer type generalization of jain and pethe operators in the last section we also propose a new modification of the lupas operators and study some direct results we also give some open problems for the readers

rate of convergence of bernstein polynomials for functions with derivatives of bounded variation abstract for any x 0 1 we first prove that if x t t x on 0 1 then the bernstein polynomials of x satisfy the asymptotic relation k 0 n k n x k n x k 1 x n k 2x 1 x 1 2 1 n o 1 n this asymptotic relation is then used to study the rate of convergence of bernstein polynomials for functions with derivatives of bounded variation an estimate of the rate of convergence is given this estimate is asymptotically the best possible at points where is continuous

duality theory in fuzzy mathematical programming problems with fuzzy coefficients in this paper the notions of subgradient subdifferential and differential with respect to convex fuzzy mappings are investigated which provides the basis for the fuzzy extremum problem theory we consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and or sufficient optimality conditions furthermore the concept of saddle points and minimax theorems under fuzzy environment is discussed the results obtained are used to formulate the lagrangian dual of fuzzy programming under certain fuzzy convexity assumptions kkt conditions for fuzzy programming are derived and the perturbed convex fuzzy programming is considered finally these results are applied to fuzzy linear programming and fuzzy quadratic programming

approximation by bezier type of meyer konig and zeller operators in this paper we give direct inverse and equivalence approximation theorems for the bezier type of meyer konig and zeller operator with unified ditzian totik modulus w f l f t email protected email protected 1

directional derivatives and subdifferential of convex fuzzy mappings and application in convex fuzzy programming abstract in this paper we put forward the concepts of directional derivative differential and subdifferential of fuzzy mappings from r n into e 1 and discuss the characterizations of directional derivative and differential by respectively using the directional derivative and differential of two crisp functions that are determined by the fuzzy mapping and we also consider the problem of existence of directional derivative for convex fuzzy mappings and discuss the relations among directional derivative differential and subdifferential of fuzzy mappings at last we give two results of application in convex fuzzy programming

degree of approximation to function of bounded variation by bezier variant of mkz operators abstract guo approx theory appl 4 1988 9 18 introduced the integral modification of meyer konig and zeller operators m n and studied the rate of convergence for functions of bounded variation in this paper we introduce the bezier variant of these integrated mkz operators and study the rate of convergence by means of the decomposition technique of functions of bounded variation together with some results of probability theory and the exact bound of mkz basis functions recently zeng j math anal appl 219 1998 364 376 claimed to improve the results of guo and gupta approx theory appl 11 1995 106 107 but there is a major mistake in the paper of zeng for special case our main theorem gives the correct estimate on the rate of convergence over the result of zeng

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

direct estimates in simultaneous approximation for bbs operators abstract the summation integral type baskakov beta operator were introduced by gupta v gupta a note on modified baskakov type operators approx theory appl 10 3 1994 74 78 in the present paper we extend our studies and introduce the baskakov beta stancu abbr bbs operator we give the moments of these operators using hypergeometric series in the next section we derive the asymptotic formula and error estimation in simultaneous approximation in the end we propose an open problem to the readers

on certain q durrmeyer type operators very recently gupta and heping v gupta w heping the rate of convergence of q durrmeyer operators for 0 q 1 math meth appl sci 31 16 2008 1946 1955 introduced certain q durrmeyer type operators and established some approximation properties in the present paper we study some direct results for the certain q durrmeyer type operators

rate of convergence for certain families of summation integral type operators in this paper we study the rate of convergence for the iterative combinations of a certain family of linear positive operators in terms of higher order integral modulus of smoothness we have used the technique of linear approximating method namely steklov mean to prove the main result in the end we propose some other sequences of linear positive operators and obtain the recurrence formulae for the central moments voronovskaja type asymptotic formulae and error estimations

preinvex fuzzy mappings abstract in this paper we introduce the concepts of preinvex fuzzy mappings quasi preinvex fuzzy mappings and invex sets by modifying the concepts proposed by noor we also give two characterization theorems for preinvex fuzzy mappings and present some new results for preinvex fuzzy mappings strictly preinvex fuzzy mappings and quasi preinvex fuzzy mappings

convergence rate for generalized baskakov type operators we introduce the bezier variant of certain integral modification of the baskakov type operators bn 1 0 and estimate the rate of convergence of these operators for bounded functions satisfying certain growth condition

approximation for bounded functions and absolutely continuous functions by beta operators in this paper the pointwise approximation properties of beta operators n are studied to the bounded functions and the absolutely continuous functions respectively first we use the asymptotic form of the central limit theorem in probability theory to derive an asymptotic estimate on the rate of convergence of beta operators n for the bounded functions next we give the optimal estimate on the first order absolute moment of the beta operators b n email protected g by direct computations then we use this estimate and bojanic cheng khan s method combining with some analysis techniques to derive an asymptotically optimal estimate on the rate of convergence of beta operators n for the absolutely continuous functions

on invex fuzzy mappings and fuzzy variational like inequalities in this paper we first show the need for introducing invex fuzzy mappings after that we show that the concept of invex fuzzy mapping previously given by wu and xu are very restrictive and the examples presented there are not correct then we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping finally we show that the results obtained by wu and xu on the relationship between fuzzy variational like inequalities and fuzzy optimization problems are still valid using these new concepts

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

properties of b vex fuzzy mappings and applications to fuzzy optimization convexity plays a key role in operations research and fuzzy optimization theory the concept of b vex and logarithmic b vex for fuzzy mappings is introduced by relaxing the definition of convexity of a fuzzy mapping most of the basic properties of b vex fuzzy mapping are discussed and established for the nondifferentiable case necessary and sufficient conditions for b vex fuzzy mapping are presented several important results are given for nonlinear fuzzy optimization problems assuming that objective and constraint functions are b vex fuzzy mappings

fuzzy weirstrass theorem and convex fuzzy mappings the convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers the local global minimum property of real valued convex functions is extended to convex fuzzy mappings it is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given in addition the weirstrass theorem is extended from real valued functions to fuzzy mappings

convexity and semicontinuity of fuzzy mappings in this paper a criterion for the convex fuzzy mapping is obtained under the condition of upper and lower semicontinuity respectively an upper lower semicontinuous fuzzy mapping is proved which convexity is equivalent to weak convexity or b vexity satisfying a special condition

φ1 φ2 convex fuzzy mappings abstract the concepts of 1 2 convexity 1 b vexity and 1 convexity for fuzzy mappings are introduced through the so called fuzzy max order among fuzzy numbers we show that the class of 1 2 convex fuzzy mappings 1 b vex fuzzy mappings and 1 convex fuzzy mappings includes many well known classes of fuzzy mappings such as convex fuzzy mappings and preinvex fuzzy mappings as its subclasses we also give a characterization for 1 b vex fuzzy mappings by proposing the concept of 1 b vex sets in addition some basic properties of fuzzy mappings from the standpoint of convex analysis are discussed

fuzzy preinvex functions in this paper we introduce the concept of fuzzy preinvex functions and invex sets these functions are more general than convex fuzzy functions and when differentiable are fuzzy invex some different types of fuzzy preinvexity functions are defined and their properties are studied it is proved that the minimum of the fuzzy preinvex functions on the invex sets can be characterized by variational like inequalities

a note on the convergence of baskakov type operators in the present paper we estimate the rate of convergence on functions of polynomial type for some variant of the baskakov operators the form of the operator discussed in the present paper makes results helpful from the computational point of view

rate of convergence of lupas kantorovich operators based on polya distribution in the present paper we consider the kantorovich modification of lupas operators based on polya distribution we estimate the rate of convergence for absolutely continuous functions having a derivative coinciding a e with a function of bounded variation

two families of bernstein durrmeyer type operators this paper deals with two families of bernstein durrmeyer type operators that arise as integral modifications respectively from the classical bernstein operators and from bernstein type operators based on the polya distribution an important role is played by the so called genuine elements of each class the only ones that reproduce linear functions asymptotic formulae and direct convergence results are stated finally some modifications of the sequences of the families are introduced in such a way that the resulting operators reproduce linear functions and are comparable with the genuine sequences

generalization of preinvex and b vex fuzzy mappings a class of fuzzy mappings called b preinvex and strictly b preinvex fuzzy mappings is introduced by relaxing the definition of preinvexity of a fuzzy mapping similarly based on a notion of differentiability of fuzzy mappings different from the usual one the class of pseudo b vex b invex and pseudo b invex fuzzy mappings is defined as a generalization of pseudo convex invex and pseudo invex fuzzy mappings we prove that a strictly b vex or b preinvex fuzzy mapping has at most one global minimum point and that the class of b vex fuzzy mappings forms a subset of the class of quasi convex fuzzy mappings b vex resp b preinvex fuzzy mappings satisfy most of the basic properties of convex resp preinvex fuzzy mappings in addition characterizations and sufficient optimality conditions are obtained for b vex and b preinvex fuzzy mappings

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed

on fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings in this paper we first introduce the weakly invex fuzzy mappings based on weakly differentiable functions and discuss the relationships between several kinds of fuzzy generalized convex mappings then a kind of fuzzy weakly univex functions are introduced and some properties of them are investigated furthermore optimality and duality results are derived for a class of generalized convex optimization problems with fuzzy weakly univex functions

on periodic solutions of a damped wave equation in a thin domain using degree theoretic methods abstract we combine the methods of the topological degree with techniques developed by j k hale and g raugel to study the periodic solutions of a damped nonlinear hyperbolic equation in a thin domain

the complete asymptotic expansion for the meyer konig and zeller operators abstract we present the complete asymptotic expansion for the meyer konig and zeller operators m n f t x as n tends to infinity all coefficients of n k k 1 2 are calculated explicitly in terms of stirling numbers of the first and second kind

pointwise approximation by bezier variant of integrated mkz operators abstract in this paper the pointwise approximation of bezier variant of integrated mkz operators for general bounded functions is studied two estimate formulas of this type approximation are obtained the approximation of functions of bounded variation becomes a special case of the main result of this paper in the case of functions of bounded variation theorem b of the paper corrects the mistake of theorem 1 of the article v gupta degree of approximation to functions of bounded variation by bezier variant of mkz operators j math anal appl 289 2004 292 300

local approximation by a variant of bernstein durrmeyer operators abstract this paper deals with the local approximation properties of a certain variant m n of the bernstein durrmeyer operators firstly we obtain an estimate on the rate of convergence of m n by means of the decomposition technique for functions of bounded variation it will be shown that our estimate in its most convenient form corollary 2 is asymptotically optimal furthermore we derive the complete asymptotic expansion for the sequence of the operators m n as n tends to infinity

the generalized baskakov type operators the use of baskakov type operators is difficult for numerical calculation because these operators include infinite series do the operators expressed as a finite sum provide the approximation properties furthermore are they appropriate for numerical calculation in this paper in connection with these questions we define a new family of linear positive operators including finite sum by using the baskakov type operators we also give some numerical results in order to compare baskakov type operators with this new defined operator

direct results for a certain family of summation integral type operators abstract in the present paper we establish some local and global direct results for a certain family of summation integral operators b n we also estimate the rate of convergence of b n f for a function f having derivatives of bounded variation

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

a damped hyperbolic equation on thin domains for a damped hyperbolic equation in a thin domain in r3 over a bounded smooth domain in r2 it is proved that the global attractors are upper semicontinuous it is shown also that a global attractor exists in the case of the critical sobolev exponent

the durrmeyer variant of an operator defined by d d stancu in 1984 d d stancu defined a sequence of positive linear operators generalizing the bernstein polynomials in this paper a durrmeyer variant of these operators is considered we derive some basic approximation properties and present a complete asymptotic expansion for the sequence of these operators all coefficients are calculated in a concise form

rate of convergence for the modified szasz mirakyan operators on functions of bounded variation in this paper we obtain an estimate of the rate of convergence of modified szasz mirakyan operators on functions of bounded variation our result essentially improves the results due to a sahai and g prasad 1993 publ inst math beograd n s 53 73 80 and v gupta and p n agrawal 1991 publ inst math beograd n s 49 97 103

fuzzy linear spaces over valued fields abstract the concept of fuzzy linear spaces was introduced by nanda 3 the purpose of the present paper is to introduce some further concepts such as convex fuzzy sets etc in fuzzy linear spaces over any valued field

direct and inverse estimates for phillips type operators in the present paper we define the generalization of the phillips operators direct and converse theorems are established for phillips operators and its new generalization the direct theorems are given for the second order ditzian totik modulus of smoothness the inverse results are derived in the terminology of j anal math 61 1993 61 111

on the rate of convergence of the generalized szasz type operators for functions of bounded variation abstract in this article we introduce the szasz bezier operatorsn which is the modified form of the szasz mirakyan operator by means of construction of suitable functions and the methods of bojanic vuillemier j approx theory31 1981 67 79 and cheng j approx theory40 1984 226 241 using some results and techniques of probability theory we obtain the rate of convergence ofsn for functions of bounded variation our results extend and sharpen the results of cheng j approx theory40 1984 226 241 guo and khan j approx theory58 1989 90 101 for the szasz mirakyan operator

necessary and sufficient conditions for fuzzy optimality problems in this paper we define a new minimum concept for fuzzy optimization problems more general than those that exist in the literature we find necessary optimality conditions based on a new fuzzy stationary point definition and we prove that these conditions are also sufficient under new fuzzy generalized convexity notions