Stolarsky Type Inequality for Sugeno Integrals on Fuzzy Convex Functions
|
|
- Miles Grant
- 5 years ago
- Views:
Transcription
1 International Journal o Mathematical nalysis Vol., 27, no., 2-28 HIKRI Ltd, Stolarsky Type Inequality or Sugeno Integrals on Fuzzy Convex Functions Dug Hun Hong Department o Mathematics, Myongji University Yongin Kyunggido , South Korea Copyright c 26 Dug Hun Hong. This article is distributed under the Creative Commons ttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. bstract Recently, Flores-Franulič et al. [ note on uzzy integral inequality o Stolarsky type, pplied Mathematics and Computation ] proved the Stolarsky s inequality or the Sugeno integral on the special class o continuous and strictly monotone unctions. This result can be generalized to a general class o uzzy convex unctions in this paper. We also give a uzzy integral inequality based on addition. Some illustrated examples are given. Mathematics Subject Classiication: 26E5 Keywords: Fuzzy measure; Sugeno integral; Stolarsky type inequality Introduction and preliminaries number o studies have examined the Sugeno integral since its introduction in 974 [6], it has been exhaustively investigated by many authors. Ralescu and dams [2] generalized a range o uzzy measures and gave several equivalent deinitions o uzzy integrals. Wang and Klir [7] provided an overview o uzzy measure theory. Caballero and Sadarangani [2-4] proved a Hermite-Hadamard type inequality, a Cauchy type inequality, and Fritz Carlson s inequality or uzzy integrals. Román-Flores et al. [3-5] presented several new types o inequalities or
2 22 Dug Hun Hong Sugeno integeals, including a Prekopa-Leindler type inequality, a Jensen type inequality, and some convolution type inequalities. Flores-Franulič et al. [5, 6] presented Chebyshevs inequality, Stolarskys inequality or uzzy integrals. Ouyang and Fang [] generalized their main results to prove some optimal upper bounds or the Sugeno integral o monotone unction in [4]. Ouyang et al. [9] generalized a Chebyshev type inequality or uzzy integral o monotone unctions based on an arbitrary uzzy measure. Hong [7] improved on previous work presenting a Hardy-type inequality or Sugeno integrals. Hong [8] proposed a Liapunov type inequality or Sugeno integrals and ind an optimal constant or which Liapunov type inequality or Sugeno integrals holds or non-increasing concave unctions. Hong [9] proposed a Berwald type inequality and a Favard type inequality or Sugeno integrals. The purpose o this paper is to generalize the main results in [6], that is, we prove a Stolarsky type inequality or Sugeno integrals on uzzy convex unctions. We also give a uzzy integral inequality based on addition. Some examples are provided to illustrate the validity o the proposed inequalities. Deinition. Let Σ be a σ-algebra o subsets o R and let µ : Σ [, ] be a non-negative, extended real-valued set unction. We say that µ is a uzzy measure i and only i a µ =. b E, F Σ and E F imply µe µf monotonicity. c E p } Σ and E E 2 imply lim p µe p = µ p= E p continuity orm below. d E p } Σ, E E 2, and µe < imply lim p µe p = µ p= E p continuity orm above. I is a non-negative real-valued unction deined on R, then we denote by F α = x X x α} = α} the α-level o, or α >, and F = x X x > } = supp is the support o. We note that α β β} α} I µ is a uzzy measure on R, then we deine the ollowing: F µ = : [, is µ-measurable}. Deinition 2. Let µ be a uzzy measure on R, Σ. I F µ R and Σ, then the Sugeno integralor the uzzy integral o on, with respect to the uzzy measure µ, is deined as S dµ = sup [α µ F α ]. α [,
3 Stolarsky type inequality or Sugeno integrals 23 In particular, i = X then S dµ = S R dµ = sup [α µf α ] α [,. The ollowing properties o the Sugeno integral are well known and can be ound in [7]: Proposition [7]. I µ is a uzzy measure on R and, g F µ R, then i S dµ µ; ii S Kdµ = K µ or any constant K [, ; iii S dµ S gdµ, i g on ; iv µ α} α S dµ α; v µ α} α S dµ α; vi S dµ < α there exists γ < α such that µ γ} < α; vii S dµ > α there exists γ > α such that µ γ} > α. 2 Stolarsky type inequality or uzzy convex unctions Flores-Franulič et al. [6] presented the ollowing Stolarsky-type inequality or uzzy integrals under the conditions that is a continuous and strictly monotone unction. Theorem Stolarsky type inequality: monotone case [6]. Let a, b >. I : [, ] [, ] is a continuous and strictly monotone decreasing or increasing unction and µ is the Lebesgue measure on R, then the inequality S dµ S x a dµ S x b dµ holds. This result can be generalized to a general class o uzzy convex unctions in this paper. We need the ollowing lemma. Lemma. Let a, b >. I : [, ] R is a uzzy convex unction, and µ is the Lebesgue measure on R, then the inequalities } } } µ α µ x a α µ x b α and } } } µ α µ x a α + µ x b α 2
4 24 Dug Hun Hong hold. Proo. Suppose that or < α, } α = [α, α 2 ]. Then we have α = α 2 = α, and hence Similarly, suppose that } x a α = [β, β 2 ], then we have x α} = [α, α 2 ]. } x b α = [γ, γ 2 ]. x α} = [β a, β a 2 ] = [γ b, γ b 2 ]. Let x α} = [h, h 2 ]. Then we have [α, α 2 ] = [h, h 2 ], [β, β 2 ] = [h a, h a 2] and [γ, γ 2 ] = [h b, h b 2]. We now consider that µ } } } α µ x a α µ x b α = α 2 α β 2 β γ 2 γ = h 2 h h a 2 h a h b 2 h b = h a h b 2 + h b h a 2 2h and } µ α = α 2 α = β 2 γ 2 β γ = β 2 γ 2 β 2 γ + β 2 γ β γ = β 2 γ 2 γ + γ β 2 β γ 2 γ + β 2 β } } = µ x a α + µ x b α. which completes the proo. By using Lemma, we obtain the ollowing main result. We show that the condition o continuity and strictly monotonicity o can be released. Fuzzy
5 Stolarsky type inequality or Sugeno integrals 25 convexity o is suicient or validity o a Stolarsky type inequality or uzzy integrals. Theorem 2. Let a, b >. I : [, ] R is a uzzy convex unction, and µ is the Lebesgue measure on R, then the inequality S dµ S x a dµ S x b dµ holds. Proo. Let S x a such that minp ε, q ε} >. Then we have S dµ = p and S x a dµ > p ε and S x b dµ = q. nd let ε > x b dµ > q ε holds. By Proposition, there exist α and β such that α > p ε and β > q ε, µ x a α} > p ε and µ x b β} > q ε hold. By Lemma, we have } µ αβ µ µ x a x a } αβ } α > p εq ε. µ µ x b x b } αβ } β Since αβ > p εq ε, by Proposition, Since ε is arbitrary, S S dµ pq = dµ > p εq ε. S dµ S gdµ. In a similar manner, we can prove the ollowing result using Lemma. Theorem 3. Let a, b >. I : [, ] R is a uzzy convex unction, and µ is the Lebesgue measure on R, then the inequality S dµ S x a dµ + S x b dµ
6 26 Dug Hun Hong holds. In the ollowing, we present a example to illustrate the validity o Theorem 2. and 3. Example. Let x = 4x x 2, x [, ] and a = 2, b = /6. Then, a straightorward calculus with the aid o computer work shows that is iis iiis Thereore x a dµ = S.6 = S x b dµ = S dµ = S 2 xdµ = α [, x 6 x 2 dµ = dµ S α [, x x 3 dµ = [α µ4 2 x α] =.68, [α µ4x 6 x 2 α] =.39, α [, x a dµ S [α µ4x 6 3 x 2 3 α] =.6. x b dµ =.97. Example 2. Let x i x [, /4 /2 i x [/4, 3/8 x = 4x i x [3/8, /2 2 x i x [/2, ], and a =, b = 2. Then is not continuous and not monotone but is uzzy convex. straightorward calculus shows that µ x a /2} = /2 and µ x b /2} = /2, and hence by Proposition, we have S x a dµ = /2 and S x b dµ = /2. Now, a straightorward calculus shows that } α/2 µ x 2 α 2 i x [, /4], α = α/2 2 /6 i x /4, /2], α/2 2 /4 + α/4 2 i x /2, ].
7 Stolarsky type inequality or Sugeno integrals 27 By proving the equation α/2 2 /6 = α, we see that µ.4499} =.4499 and hence Thereore.4499 = S S dµ S dµ = x a dµ S x b dµ =.25. Reerences [] P. S. Bullen, Dictionary o Inequalities, ddison Wesley Longman Inc., 998. [2] J. Caballero, K. Sadarangani, Hermite-Hadamard inequality or uzzy integrals, ppl. Math. Comput., 25 29, [3] J. Caballero, K. Sadarangani, Fritz Carlson s inequality or uzzy integrals, Computers and Math. with ppl., 59 2, [4] J. Caballero, K. Sadarangani, Cauchy-Schwarz type inequality or uzzy integrals, Nonlinear nalysis: Theory, Methods and pplications, 73 2, [5]. Flores-Franulič, H. Román-Flores, Chebyshev type inequality or uzzy integrals, ppl. Math. Comput., 9 27, [6]. Flores-Franulič, H. Román-Flores, Y. Chalco-Cano, note on uzzy integral inequality o Stolarsky type, ppl. Math. Comput., 96 28, [7] D. H. Hong, sharp Hardy-type inequality or Sugeno integrals, ppl. Math. Comput., 27 2, [8] D. H. Hong, Liapunov type inequality or Sugeno integrals, Nonlinear nalysis: Theory, Methods and pplications, 27 2,
8 28 Dug Hun Hong [9] D. H. Hong, Berward and Favard type inequalities or Fuzzy integrals, Int. Journal o Uncertainty, Fuzziness and Knowledge-Based Systems, 24 26, [] Y. Ouyang, J. Fang, Sugeno integral or monotone unctions based on Lebesgue measure, Computers and Mathematics with pplications, 56 28, [] Y. Ouyang, J. Fang, L. Wang, Fuzzy Chebyshev type inequality, Int. J. pprox., 48 28, [2] D. Ralescu, G. dams, The uzzy integral, J. Math. nal. ppl., 75 98, [3] H. Román-Flores,. Flores-Franulič, Y. Chalco-Cano, Hardy type inequality or uzzy integrals, ppl. Math. Comput., 24 28, [4] H. Román-Flores,. Flores-Franulič, Y. Chalco-Cano, Jensen type inequality or uzzy integrals, Inorm. Sci., 77 27, [5] H. Román-Flores,. Flores-Franulič, Y. Chalco-Cano, convolution type inequality or uzzy integrals, ppl. Math. Comput., 95 28, [6] M. Sugeno, Theory o Fuzzy Integrals and Its pplications, Ph.D. Thesis, Tokyo Institute o Technology, 974. [7] Z. Wang, G. Klir, Fuzzy Measure Theory, Springer, New York, Received: December 6, 26; Published: January, 27
A Note on Gauss Type Inequality for Sugeno Integrals
pplied Mathematical Sciences, Vol., 26, no. 8, 879-885 HIKRI Ltd, www.m-hikari.com http://d.doi.org/.2988/ams.26.63 Note on Gauss Type Inequality for Sugeno Integrals Dug Hun Hong Department of Mathematics,
More informationResearch Article General Fritz Carlson s Type Inequality for Sugeno Integrals
Hindawi Publishing Corporation Journal of Inequalities and pplications Volume, rticle ID 7643, 9 pages doi:.55//7643 Research rticle General Fritz Carlson s Type Inequality for Sugeno Integrals Xiaojing
More informationNote on the Expected Value of a Function of a Fuzzy Variable
International Journal of Mathematical Analysis Vol. 9, 15, no. 55, 71-76 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.1988/ijma.15.5145 Note on the Expected Value of a Function of a Fuzzy Variable
More informationGENERAL RELATED JENSEN TYPE INEQUALITIES FOR FUZZY INTEGRALS
TWMS J. App. Eng. Math. V.8, N., 08, pp. -7 GENERAL RELATED JENSEN TYPE INEQUALITIES FOR FUZZY INTEGRALS B. DARABY, Abstract. In this paper, related inequalities to Jensen type inequality for the seminormed
More informationFURTHER DEVELOPMENT OF CHEBYSHEV TYPE INEQUALITIES FOR SUGENO INTEGRALS AND T-(S-)EVALUATORS
K Y BERNETIK VOLUM E 46 21, NUMBER 1, P GES 83 95 FURTHER DEVELOPMENT OF CHEBYSHEV TYPE INEQULITIES FOR SUGENO INTEGRLS ND T-S-EVLUTORS Hamzeh gahi, Radko Mesiar and Yao Ouyang In this paper further development
More informationSOME CHARACTERIZATIONS OF HARMONIC CONVEX FUNCTIONS
International Journal o Analysis and Applications ISSN 2291-8639 Volume 15, Number 2 2017, 179-187 DOI: 10.28924/2291-8639-15-2017-179 SOME CHARACTERIZATIONS OF HARMONIC CONVEX FUNCTIONS MUHAMMAD ASLAM
More informationAdditive functional inequalities in Banach spaces
Lu and Park Journal o Inequalities and Applications 01, 01:94 http://www.journaloinequalitiesandapplications.com/content/01/1/94 R E S E A R C H Open Access Additive unctional inequalities in Banach spaces
More information-Complement of Intuitionistic. Fuzzy Graph Structure
International Mathematical Forum, Vol. 12, 2017, no. 5, 241-250 HIKRI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.612171 -Complement of Intuitionistic Fuzzy Graph Structure Vandana ansal Department
More informationChebyshev Type Inequalities for Sugeno Integrals with Respect to Intuitionistic Fuzzy Measures
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 9, No 2 Sofia 2009 Chebyshev Type Inequalities for Sugeno Integrals with Respect to Intuitionistic Fuzzy Measures Adrian I.
More informationA Generalization of Generalized Triangular Fuzzy Sets
International Journal of Mathematical Analysis Vol, 207, no 9, 433-443 HIKARI Ltd, wwwm-hikaricom https://doiorg/02988/ijma2077350 A Generalization of Generalized Triangular Fuzzy Sets Chang Il Kim Department
More informationA Novel Approach: Soft Groups
International Journal of lgebra, Vol 9, 2015, no 2, 79-83 HIKRI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ija2015412121 Novel pproach: Soft Groups K Moinuddin Faculty of Mathematics, Maulana zad National
More informationInternational Journal of Approximate Reasoning
JID:IJ ID:808 /FL [mg; v.; Prn:4/08/20; :2] P. (-2) International Journal of pproximate Reasoning ( ) Contents lists available at ScienceDirect International Journal of pproximate Reasoning 4 4 www.elsevier.com/locate/iar
More informationOn a Certain Representation in the Pairs of Normed Spaces
Applied Mathematical Sciences, Vol. 12, 2018, no. 3, 115-119 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.712362 On a Certain Representation in the Pairs of ormed Spaces Ahiro Hoshida
More informationInequalities for Convex and Non-Convex Functions
pplied Mathematical Sciences, Vol. 8, 204, no. 9, 5923-593 HIKRI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.204.4860 Inequalities for Convex and Non-Convex Functions Zlatko Pavić Mechanical Engineering
More informationOn Symmetric Bi-Multipliers of Lattice Implication Algebras
International Mathematical Forum, Vol. 13, 2018, no. 7, 343-350 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2018.8423 On Symmetric Bi-Multipliers of Lattice Implication Algebras Kyung Ho
More informationJoin Reductions and Join Saturation Reductions of Abstract Knowledge Bases 1
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 3, 109-115 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.7312 Join Reductions and Join Saturation Reductions
More informationDerivation, f-derivation and generalized derivation of KUS-algebras
PURE MATHEMATICS RESEARCH ARTICLE Derivation, -derivation and generalized derivation o KUS-algebras Chiranjibe Jana 1 *, Tapan Senapati 2 and Madhumangal Pal 1 Received: 08 February 2015 Accepted: 10 June
More informationLogarithm of a Function, a Well-Posed Inverse Problem
American Journal o Computational Mathematics, 4, 4, -5 Published Online February 4 (http://www.scirp.org/journal/ajcm http://dx.doi.org/.436/ajcm.4.4 Logarithm o a Function, a Well-Posed Inverse Problem
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationCaristi-type Fixed Point Theorem of Set-Valued Maps in Metric Spaces
International Journal of Mathematical Analysis Vol. 11, 2017, no. 6, 267-275 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.717 Caristi-type Fixed Point Theorem of Set-Valued Maps in Metric
More informationKey Renewal Theory for T -iid Random Fuzzy Variables
Applied Mathematical Sciences, Vol. 3, 29, no. 7, 35-329 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ams.29.9236 Key Renewal Theory for T -iid Random Fuzzy Variables Dug Hun Hong Department of Mathematics,
More informationPartial Averaging of Fuzzy Differential Equations with Maxima
Advances in Dynamical Systems and Applications ISSN 973-5321, Volume 6, Number 2, pp. 199 27 211 http://campus.mst.edu/adsa Partial Averaging o Fuzzy Dierential Equations with Maxima Olga Kichmarenko and
More informationProblem Set. Problems on Unordered Summation. Math 5323, Fall Februray 15, 2001 ANSWERS
Problem Set Problems on Unordered Summation Math 5323, Fall 2001 Februray 15, 2001 ANSWERS i 1 Unordered Sums o Real Terms In calculus and real analysis, one deines the convergence o an ininite series
More informationBounded Subsets of the Zygmund F -Algebra
International Journal of Mathematical Analysis Vol. 12, 2018, no. 9, 425-431 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2018.8752 Bounded Subsets of the Zygmund F -Algebra Yasuo Iida Department
More informationContinuous Solutions of a Functional Equation Involving the Harmonic and Arithmetic Means
Continuous Solutions o a Functional Equation Involving the Harmonic and Arithmetic Means Rebecca Whitehead and Bruce Ebanks aculty advisor) Department o Mathematics and Statistics Mississippi State University
More informationHyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation on a Restricted Domain
Int. Journal of Math. Analysis, Vol. 7, 013, no. 55, 745-75 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.013.394 Hyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation
More informationA Remark on Certain Filtrations on the Inner Automorphism Groups of Central Division Algebras over Local Number Fields
International Journal of lgebra, Vol. 10, 2016, no. 2, 71-79 HIKRI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.612 Remark on Certain Filtrations on the Inner utomorphism Groups of Central
More informationSemideterministic Finite Automata in Operational Research
Applied Mathematical Sciences, Vol. 0, 206, no. 6, 747-759 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.206.62 Semideterministic Finite Automata in Operational Research V. N. Dumachev and
More informationTwo Constants of Motion in the Generalized Damped Oscillator
Advanced Studies in Theoretical Physics Vol. 10, 2016, no. 2, 57-65 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2016.511107 Two Constants o Motion in the Generalized Damped Oscillator
More informationA Disaggregation Approach for Solving Linear Diophantine Equations 1
Applied Mathematical Sciences, Vol. 12, 2018, no. 18, 871-878 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.8687 A Disaggregation Approach for Solving Linear Diophantine Equations 1 Baiyi
More informationExample: When describing where a function is increasing, decreasing or constant we use the x- axis values.
Business Calculus Lecture Notes (also Calculus With Applications or Business Math II) Chapter 3 Applications o Derivatives 31 Increasing and Decreasing Functions Inormal Deinition: A unction is increasing
More informationSome Hermite-Hadamard type integral inequalities for operator AG-preinvex functions
Acta Univ. Sapientiae, Mathematica, 8, (16 31 33 DOI: 1.1515/ausm-16-1 Some Hermite-Hadamard type integral inequalities or operator AG-preinvex unctions Ali Taghavi Department o Mathematics, Faculty o
More informationWeighted Composition Followed by Differentiation between Weighted Bergman Space and H on the Unit Ball 1
International Journal of Mathematical Analysis Vol 9, 015, no 4, 169-176 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/ijma015411348 Weighted Composition Followed by Differentiation between Weighted
More informationConvex Sets Strict Separation in Hilbert Spaces
Applied Mathematical Sciences, Vol. 8, 2014, no. 64, 3155-3160 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.44257 Convex Sets Strict Separation in Hilbert Spaces M. A. M. Ferreira 1
More informationThe Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces
Applied Mathematical Sciences, Vol. 11, 2017, no. 12, 549-560 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.718 The Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive
More informationHermite-Hadamard Type Inequalities for Fractional Integrals
International Journal of Mathematical Analysis Vol., 27, no. 3, 625-634 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ijma.27.7577 Hermite-Hadamard Type Inequalities for Fractional Integrals Loredana
More informationThe Greatest Common Divisor of k Positive Integers
International Mathematical Forum, Vol. 3, 208, no. 5, 25-223 HIKARI Ltd, www.m-hiari.com https://doi.org/0.2988/imf.208.822 The Greatest Common Divisor of Positive Integers Rafael Jaimczu División Matemática,
More informationOn Toader-Sándor Mean 1
International Mathematical Forum, Vol. 8, 213, no. 22, 157-167 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/imf.213.3344 On Toader-Sándor Mean 1 Yingqing Song College of Mathematics and Computation
More informationOn Picard value problem of some difference polynomials
Arab J Math 018 7:7 37 https://doiorg/101007/s40065-017-0189-x Arabian Journal o Mathematics Zinelâabidine Latreuch Benharrat Belaïdi On Picard value problem o some dierence polynomials Received: 4 April
More informationResearch Article Fuzzy Parameterized Soft Expert Set
Abstract and Applied Analysis Volume 2012 Article ID 258361 15 pages doi:10.1155/2012/258361 Research Article uzzy Parameterized Soft Expert Set Maruah Bashir and Abdul Razak Salleh School of Mathematical
More informationResearch Article Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces
Abstract and Applied Analysis Volume 2012, Article ID 435790, 6 pages doi:10.1155/2012/435790 Research Article Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly
More informationHomomorphism on T Anti-Fuzzy Ideals of Ring
International Journal o Computational Science and Mathematics. ISSN 0974-3189 Volume 8, Number 1 (2016), pp. 35-48 International esearch Publication House http://www.irphouse.com Homomorphism on T nti-fuzzy
More informationOn Non-metric Covering Lemmas and Extended Lebesgue-differentiation Theorem
British Journal of Mathematics & Computer Science 8(3): 220-228, 205, rticle no.bjmcs.205.56 ISSN: 223-085 SCIENCEDOMIN international www.sciencedomain.org On Non-metric Covering Lemmas and Extended Lebesgue-differentiation
More informationTrace inequalities for positive semidefinite matrices with centrosymmetric structure
Zhao et al Journal of Inequalities pplications 1, 1:6 http://wwwjournalofinequalitiesapplicationscom/content/1/1/6 RESERCH Trace inequalities for positive semidefinite matrices with centrosymmetric structure
More informationk-pell, k-pell-lucas and Modified k-pell Numbers: Some Identities and Norms of Hankel Matrices
International Journal of Mathematical Analysis Vol. 9, 05, no., 3-37 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.4370 k-pell, k-pell-lucas and Modified k-pell Numbers: Some Identities
More informationComplete and Fuzzy Complete d s -Filter
International Journal of Mathematical Analysis Vol. 11, 2017, no. 14, 657-665 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.7684 Complete and Fuzzy Complete d s -Filter Habeeb Kareem
More informationNew Iterative Algorithm for Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 20, 995-1003 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4392 New Iterative Algorithm for Variational Inequality Problem and Fixed
More information18.175: Lecture 3 Integration
18.175: Lecture 3 Scott Sheffield MIT Outline Outline Recall definitions Probability space is triple (Ω, F, P) where Ω is sample space, F is set of events (the σ-algebra) and P : F [0, 1] is the probability
More informationCrisp Profile Symmetric Decomposition of Fuzzy Numbers
Applied Mathematical Sciences, Vol. 10, 016, no. 8, 1373-1389 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.016.59598 Crisp Profile Symmetric Decomposition of Fuzzy Numbers Maria Letizia Guerra
More informationA Fixed Point Approach to the Stability of a Quadratic-Additive Type Functional Equation in Non-Archimedean Normed Spaces
International Journal of Mathematical Analysis Vol. 9, 015, no. 30, 1477-1487 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.1988/ijma.015.53100 A Fied Point Approach to the Stability of a Quadratic-Additive
More informationNON-ARCHIMEDEAN BANACH SPACE. ( ( x + y
J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. ISSN(Print 6-0657 https://doi.org/0.7468/jksmeb.08.5.3.9 ISSN(Online 87-608 Volume 5, Number 3 (August 08, Pages 9 7 ADDITIVE ρ-functional EQUATIONS
More informationarxiv: v1 [math.oc] 1 Apr 2012
arxiv.tex; October 31, 2018 On the extreme points o moments sets arxiv:1204.0249v1 [math.oc] 1 Apr 2012 Iosi Pinelis Department o Mathematical ciences Michigan Technological University Houghton, Michigan
More informationResearch Article On Decomposable Measures Induced by Metrics
Applied Mathematics Volume 2012, Article ID 701206, 8 pages doi:10.1155/2012/701206 Research Article On Decomposable Measures Induced by Metrics Dong Qiu 1 and Weiquan Zhang 2 1 College of Mathematics
More informationFunctional Form of the Jensen and the Hermite-Hadamard Inequality
Applied Mathematical Sciences, Vol. 9, 2015, no. 4, 149-159 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.411888 Functional Form of the Jensen and the Hermite-Hadamard Inequality Zlatko
More informationBasic mathematics of economic models. 3. Maximization
John Riley 1 January 16 Basic mathematics o economic models 3 Maimization 31 Single variable maimization 1 3 Multi variable maimization 6 33 Concave unctions 9 34 Maimization with non-negativity constraints
More informationNew Nonlinear Conditions for Approximate Sequences and New Best Proximity Point Theorems
Applied Mathematical Sciences, Vol., 207, no. 49, 2447-2457 HIKARI Ltd, www.m-hikari.com https://doi.org/0.2988/ams.207.7928 New Nonlinear Conditions for Approximate Sequences and New Best Proximity Point
More informationKKM-Type Theorems for Best Proximal Points in Normed Linear Space
International Journal of Mathematical Analysis Vol. 12, 2018, no. 12, 603-609 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2018.81069 KKM-Type Theorems for Best Proximal Points in Normed
More informationSome Properties of a Semi Dynamical System. Generated by von Forester-Losata Type. Partial Equations
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 38, 1863-1868 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.3481 Some Properties of a Semi Dynamical System Generated by von Forester-Losata
More informationFixed Points for Multivalued Mappings in b-metric Spaces
Applied Mathematical Sciences, Vol. 10, 2016, no. 59, 2927-2944 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.68225 Fixed Points for Multivalued Mappings in b-metric Spaces Seong-Hoon
More informationSharp Bounds for Seiffert Mean in Terms of Arithmetic and Geometric Means 1
Int. Journal of Math. Analysis, Vol. 7, 01, no. 6, 1765-177 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.01.49 Sharp Bounds for Seiffert Mean in Terms of Arithmetic and Geometric Means 1
More informationSymmetric Properties for the (h, q)-tangent Polynomials
Adv. Studies Theor. Phys., Vol. 8, 04, no. 6, 59-65 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/astp.04.43 Symmetric Properties for the h, q-tangent Polynomials C. S. Ryoo Department of Mathematics
More informationAPPROXIMATE ADDITIVE MAPPINGS IN 2-BANACH SPACES AND RELATED TOPICS: REVISITED. Sungsik Yun
Korean J. Math. 3 05, No. 3, pp. 393 399 http://dx.doi.org/0.568/kjm.05.3.3.393 APPROXIMATE ADDITIVE MAPPINGS IN -BANACH SPACES AND RELATED TOPICS: REVISITED Sungsik Yun Abstract. W. Park [J. Math. Anal.
More informationSOME HERMITE HADAMARD TYPE INEQUALITIES FOR THE PRODUCT OF TWO OPERATOR PREINVEX FUNCTIONS
Banach J. Math. Anal. 9 15), no., uncorrected galleyproo DOI: 1.1535/bjma/9-- ISSN: 1735-8787 electronic) www.emis.de/journals/bjma/ SOME HERMITE HADAMARD TYPE INEQUALITIES FOR THE PRODUCT OF TWO OPERATOR
More informationResearch Article On λ-statistically Convergent Double Sequences of Fuzzy Numbers
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008, Article ID 47827, 6 pages doi:0.55/2008/47827 Research Article On λ-statistically Convergent Double Sequences of Fuzzy
More informationSTATISTICALLY CONVERGENT TRIPLE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTION
Journal o athematical Analysis ISSN: 227-342, URL: http://www.ilirias.com Volume 4 Issue 2203), Pages 6-22. STATISTICALLY CONVERGENT TRIPLE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTION AAR JYOTI DUTTA, AYHAN
More informationStability of a Functional Equation Related to Quadratic Mappings
International Journal of Mathematical Analysis Vol. 11, 017, no., 55-68 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.017.610116 Stability of a Functional Equation Related to Quadratic Mappings
More informationTHEOREMS, ETC., FOR MATH 515
THEOREMS, ETC., FOR MATH 515 Proposition 1 (=comment on page 17). If A is an algebra, then any finite union or finite intersection of sets in A is also in A. Proposition 2 (=Proposition 1.1). For every
More information9.3 Graphing Functions by Plotting Points, The Domain and Range of Functions
9. Graphing Functions by Plotting Points, The Domain and Range o Functions Now that we have a basic idea o what unctions are and how to deal with them, we would like to start talking about the graph o
More informationA Note of the Strong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 10, 2016, no. 6, 255-261 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.511700 A Note of the Strong Convergence of the Mann Iteration for Demicontractive
More informationExplicit Expressions for Free Components of. Sums of the Same Powers
Applied Mathematical Sciences, Vol., 27, no. 53, 2639-2645 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ams.27.79276 Explicit Expressions for Free Components of Sums of the Same Powers Alexander
More informationSection Integration of Nonnegative Measurable Functions
18.2. Integration of Nonnegative Measurable Functions 1 Section 18.2. Integration of Nonnegative Measurable Functions Note. We now define integrals of measurable functions on measure spaces. Though similar
More informationSecure Weakly Convex Domination in Graphs
Applied Mathematical Sciences, Vol 9, 2015, no 3, 143-147 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ams2015411992 Secure Weakly Convex Domination in Graphs Rene E Leonida Mathematics Department
More informationSome generalized Hermite-Hadamard type integral inequalities for generalized s-convex functions on fractal sets
Kılıçman Saleh Advances in Dierence Equations 05 05:30 DOI 086/s366-05-0639-8 R E S E A R C H Open Access Some generalized Hermite-Hadamard type integral inequalities or generalized s-convex unctions on
More informationStrong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 9, 015, no. 4, 061-068 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.5166 Strong Convergence of the Mann Iteration for Demicontractive Mappings Ştefan
More informationGROWTH PROPERTIES OF COMPOSITE ANALYTIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES IN UNIT POLYDISC FROM THE VIEW POINT OF THEIR NEVANLINNA L -ORDERS
Palestine Journal o Mathematics Vol 8209 346 352 Palestine Polytechnic University-PPU 209 GROWTH PROPERTIES OF COMPOSITE ANALYTIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES IN UNIT POLYDISC FROM THE VIEW POINT
More informationBounds Improvement for Neuman-Sándor Mean Using Arithmetic, Quadratic and Contraharmonic Means 1
International Mathematical Forum, Vol. 8, 2013, no. 30, 1477-1485 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.36125 Bounds Improvement for Neuman-Sándor Mean Using Arithmetic, Quadratic
More informationAn Averaging Result for Fuzzy Differential Equations with a Small Parameter
Annual Review o Chaos Theory, Biurcations and Dynamical Systems Vol. 5, 215 1-9, www.arctbds.com. Copyright c 215 ARCTBDS. SSN 2253 371. All Rights Reserved. An Averaging Result or Fuzzy Dierential Equations
More informationRefinement of Steffensen s Inequality for Superquadratic functions
Int. Journal of Math. Analysis, Vol. 8, 14, no. 13, 611-617 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.1988/ijma.14.45 Refinement of Steffensen s Inequality for Superquadratic functions Mohammed
More informationResearch Article Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means
Applied Mathematics Volume 2012, Article ID 480689, 8 pages doi:10.1155/2012/480689 Research Article Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and
More informationA Note on Multiplicity Weight of Nodes of Two Point Taylor Expansion
Applied Mathematical Sciences, Vol, 207, no 6, 307-3032 HIKARI Ltd, wwwm-hikaricom https://doiorg/02988/ams2077302 A Note on Multiplicity Weight of Nodes of Two Point Taylor Expansion Koichiro Shimada
More informationA Direct Proof of Caristi s Fixed Point Theorem
Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289-2294 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.66190 A Direct Proof of Caristi s Fixed Point Theorem Wei-Shih Du Department
More informationSome spaces of sequences of interval numbers defined by a modulus function
Global Journal o athematical Analysis, 2 1 2014 11-16 c Science Publishing Corporation wwwsciencepubcocom/inexphp/gja oi: 1014419/gjmav2i12005 Research Paper Some spaces o sequences o interval numbers
More informationA Stability Result for Fixed Point Iteration in Partial Metric Space
International Journal of Mathematical Analysis Vol. 9, 2015, no. 52, 2591-2597 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.58188 A Stability Result for Fixed Point Iteration in Partial
More informationPermanents and Determinants of Tridiagonal Matrices with (s, t)-pell Numbers
International Mathematical Forum, Vol 12, 2017, no 16, 747-753 HIKARI Ltd, wwwm-hikaricom https://doiorg/1012988/imf20177652 Permanents and Determinants of Tridiagonal Matrices with (s, t)-pell Numbers
More informationDecompositions of Balanced Complete Bipartite Graphs into Suns and Stars
International Journal of Contemporary Mathematical Sciences Vol. 13, 2018, no. 3, 141-148 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2018.8515 Decompositions of Balanced Complete Bipartite
More informationHermite-Hadamard Type Inequalities for Fractional Integrals Operators
Applied Mathematical Sciences, Vol., 27, no. 35, 745-754 HIKARI Ltd, www.m-hiari.com https://doi.org/.2988/ams.27.7573 Hermite-Hadamard Type Inequalities for ractional Integrals Operators Loredana Ciurdariu
More informationDiophantine Equations. Elementary Methods
International Mathematical Forum, Vol. 12, 2017, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.7223 Diophantine Equations. Elementary Methods Rafael Jakimczuk División Matemática,
More informationSums of Tribonacci and Tribonacci-Lucas Numbers
International Journal of Mathematical Analysis Vol. 1, 018, no. 1, 19-4 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.018.71153 Sums of Tribonacci Tribonacci-Lucas Numbers Robert Frontczak
More informationLecture 4 Lebesgue spaces and inequalities
Lecture 4: Lebesgue spaces and inequalities 1 of 10 Course: Theory of Probability I Term: Fall 2013 Instructor: Gordan Zitkovic Lecture 4 Lebesgue spaces and inequalities Lebesgue spaces We have seen how
More informationPositive Solution of a Nonlinear Four-Point Boundary-Value Problem
Nonlinear Analysis and Differential Equations, Vol. 5, 27, no. 8, 299-38 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/nade.27.78 Positive Solution of a Nonlinear Four-Point Boundary-Value Problem
More informationEquivalence of K-Functionals and Modulus of Smoothness Generated by the Weinstein Operator
International Journal of Mathematical Analysis Vol. 11, 2017, no. 7, 337-345 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2017.7219 Equivalence of K-Functionals and Modulus of Smoothness
More informationFuzzy Sequences in Metric Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 15, 699-706 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4262 Fuzzy Sequences in Metric Spaces M. Muthukumari Research scholar, V.O.C.
More informationThe Split Hierarchical Monotone Variational Inclusions Problems and Fixed Point Problems for Nonexpansive Semigroup
International Mathematical Forum, Vol. 11, 2016, no. 8, 395-408 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2016.6220 The Split Hierarchical Monotone Variational Inclusions Problems and
More informationMorphisms Between the Groups of Semi Magic Squares and Real Numbers
International Journal of Algebra, Vol. 8, 2014, no. 19, 903-907 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2014.212137 Morphisms Between the Groups of Semi Magic Squares and Real Numbers
More informationOn (m,n)-ideals in LA-Semigroups
Applied Mathematical Sciences, Vol. 7, 2013, no. 44, 2187-2191 HIKARI Ltd, www.m-hikari.com On (m,n)-ideals in LA-Semigroups Muhammad Akram University of Gujrat Gujrat, Pakistan makram 69@yahoo.com Naveed
More informationOn additions of interactive fuzzy numbers
On additions o interactive uzzy numbers Christer Carlsson IAMSR, Åbo Akademi University, Lemminkäinengatan 14B, FIN-20520 Åbo, Finland e-mail: christer.carlsson@abo.i Robert Fullér Department o Operations
More informationOn Optimality Conditions for Pseudoconvex Programming in Terms of Dini Subdifferentials
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 18, 891-898 HIKARI Ltd, www.m-hikari.com On Optimality Conditions for Pseudoconvex Programming in Terms of Dini Subdifferentials Jaddar Abdessamad Mohamed
More informationStrong Lyapunov Functions for Systems Satisfying the Conditions of La Salle
06 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 49, NO. 6, JUNE 004 Strong Lyapunov Functions or Systems Satisying the Conditions o La Salle Frédéric Mazenc and Dragan Ne sić Abstract We present a construction
More informationAn Application of Fibonacci Sequence on Continued Fractions
International Mathematical Forum, Vol. 0, 205, no. 2, 69-74 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/imf.205.42207 An Application of Fibonacci Sequence on Continued Fractions Ali H. Hakami
More informationYURI LEVIN AND ADI BEN-ISRAEL
Pp. 1447-1457 in Progress in Analysis, Vol. Heinrich G W Begehr. Robert P Gilbert and Man Wah Wong, Editors, World Scientiic, Singapore, 003, ISBN 981-38-967-9 AN INVERSE-FREE DIRECTIONAL NEWTON METHOD
More information