06487nam 2200481 450 99646655680331620230619212002.03-030-90563-2(MiAaPQ)EBC6942688(Au-PeEL)EBL6942688(CKB)21441191700041(PPN)261524097(EXLCZ)992144119170004120221112d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNew perspectives on the theory of inequalities for integral and sum /Nazia Irshad [and three others]Cham, Switzerland :Springer International Publishing,[2022]©20221 online resource (319 pages)Print version: Irshad, Nazia New Perspectives on the Theory of Inequalities for Integral and Sum Cham : Springer International Publishing AG,c2022 9783030905620 Intro -- Preface -- Contents -- Notations and Terminologies -- 1 Linear Inequalities via Interpolation Polynomials and Green Functions -- 1.1 Linear Inequalities and the Extension of Montgomery Identity with New Green Functions -- 1.1.1 Results Obtained by the Extension of Montgomery Identity and New Green Functions -- 1.1.2 Inequalities for n-Convex Functions at a Point -- 1.1.3 Bounds for Remainders and Functionals -- 1.1.4 Mean Value Theorems -- 1.2 Linear Inequalities and the Taylor Formula with New Green Functions -- 1.2.1 Results Obtained by the Taylor Formula and New Green Functions -- 1.2.2 Inequalities for n-Convex Functions at a Point -- 1.2.3 Bounds for Remainders and Functionals -- 1.2.4 Mean Value Theorems and Exponential Convexity -- Mean Value Theorems -- Logarithmically Convex Functions -- n-Exponentially Convex Functions -- 1.2.5 Examples with Applications -- 1.3 Linear Inequalities and Hermite Interpolation with New Green Functions -- 1.3.1 Results Obtained by the Hermite Interpolation Polynomial and Green Functions -- 1.3.2 Inequalities for n-Convex Functions at a Point -- 1.3.3 Bounds for Remainders and Functionals -- 1.4 Linear Inequalities and the Fink Identity with New Green Functions -- 1.4.1 Results Obtained by the Fink identity and New Green functions -- 1.4.2 Inequalities for n-Convex Functions at a Point -- 1.4.3 Bounds for Remainders and Functionals -- 1.5 Linear Inequalities and the Abel-Gontscharoff's Interpolation Polynomial -- 1.5.1 Results Obtained by the Abel-Gontscharoff's Interpolation -- 1.5.2 Results Obtained by the Abel-Gontscharoff's Interpolation Polynomial and Green Functions -- 1.5.3 Inequalities for n-Convex Functions at a Point -- 1.5.4 Bounds for Remainders and Functionals -- 2 Ostrowski Inequality -- 2.1 Generalized Ostrowski Type Inequalities with Parameter.2.1.1 Ostrowski Type Inequality for Bounded Differentiable Functions -- 2.1.2 Ostrowski Type Inequalities for Bounded Below Only and Bounded Above Only Differentiable Functions -- 2.1.3 Applications to Numerical Integration -- 2.2 Generalized Ostrowski Type Inequalities for Functions of Lp Spaces and Bounded Variation -- 2.2.1 Ostrowski Type Inequality for Functions of Lp Spaces -- 2.2.2 Ostrowski Type Inequality for Functions of Bounded Variation -- 2.2.3 Applications to Numerical Integration -- 2.3 Generalized Weighted Ostrowski Type Inequality with Parameter -- 2.3.1 Weighted Ostrowski Type Inequality with Parameter -- 2.3.2 Applications to Numerical Integration -- 2.4 Generalized Weighted Ostrowski-Grüss Type Inequality with Parameter -- 2.4.1 Weighted Ostrowski-Grüss Type Inequality with Parameter by Using Korkine's Identity -- 2.4.2 Applications to Probability Theory -- 2.4.3 Applications to Numerical Integration -- 2.5 Generalized Fractional Ostrwoski Type Inequality with Parameter -- 2.5.1 Fractional Ostrowski Type Inequality Involving Parameter -- 2.6 Generalized Inequalities for Functions of Lp Spaces via Montgomery Identity with Parameters -- 2.6.1 Montgomery Identity for Functions of Two Variables involving Parameters -- 2.6.2 Generalized Ostrowski Type Inequality -- 2.6.3 Generalized Grüss Type Inequalities -- 3 Functions with Nondecreasing Increments -- 3.1 Functions with Nondecreasing Increments in Real Life -- 3.2 Relationship Among Functions with Nondecreasing Increments and Many Others -- 3.3 Functions with Nondecreasing Increments of Order 3 -- 3.3.1 On Levinson Type Inequalities -- 3.3.2 On Jensen-Mercer Type Inequalities -- 4 Popoviciu and Čebyšev-Popoviciu Type Identities and Inequalities -- 4.1 Linear Inequalities for Higher Order -Convex and Completely Monotonic Functions.4.1.1 Discrete Identity for Two Dimensional Sequences -- 4.1.2 Discrete Identity and Inequality for Functions of Two Variables -- 4.1.3 Integral Identity and Inequality for Functions of One Variable -- 4.1.4 Integral Identity and Inequality for Functions of Two Variables -- 4.1.5 Mean Value Theorems and Exponential Convexity -- Mean Value Theorems -- Exponential Convexity -- Examples of Completely Monotonic and Exponentially Convex Functions -- 4.2 Generalized Čebyšev and Ky Fan Identities and Inequalities for -Convex Functions -- 4.2.1 Generalized Discrete Čebyšev Identity and Inequality -- 4.2.2 Generalized Integral Čebyšev Identity and Inequality -- 4.2.3 Generalized Integral Ky Fan Identity and Inequality -- 4.3 Weighted Montgomery Identities for Higher Order Differentiable Function of Two Variables and Related Inequalities -- 4.3.1 Montgomery Identities for Double Weighted Integrals of Higher Order Differentiable Functions -- Special Cases -- 4.3.2 Ostrowski Type Inequalities for Double Weighted Integrals of Higher Order Differentiable Functions -- 4.3.3 Grüss Type Inequalities for Double Weighted Integrals of Higher Order Differentiable Functions -- Bibliography -- Index.Inequalities (Mathematics)Inequalities (Mathematics)Data processingDesigualtats (Matemàtica)thubLlibres electrònicsthubInequalities (Mathematics)Inequalities (Mathematics)Data processing.Desigualtats (Matemàtica)515.243Irshad NaziaMiAaPQMiAaPQMiAaPQBOOK996466556803316New perspectives on the theory of inequalities for integral and sum2968978UNISA03613nam 22006855 450 991030075200332120200702005227.09781484235799148423579710.1007/978-1-4842-3579-9(CKB)4100000005679063(DE-He213)978-1-4842-3579-9(MiAaPQ)EBC5494721(CaSebORM)9781484235799(PPN)229919707(OCoLC)1051771109(OCoLC)on1051771109(EXLCZ)99410000000567906320180816d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierBeginning Apache Spark 2 With Resilient Distributed Datasets, Spark SQL, Structured Streaming and Spark Machine Learning library /by Hien Luu1st ed. 2018.Berkeley, CA :Apress :Imprint: Apress,2018.1 online resource (XI, 393 p. 86 illus.)Includes index.9781484235782 1484235789 1. Introduction to Apache Spark -- 2. Working with Apache Spark -- 3. Resilient Distributed Dataset -- 4. Spark SQL - Foundation -- 5. Spark SQL - Advanced -- 6. Spark Streaming -- 7. Spark Streaming Advanced -- 8. Machine Learning with Spark.Develop applications for the big data landscape with Spark and Hadoop. This book also explains the role of Spark in developing scalable machine learning and analytics applications with Cloud technologies. Beginning Apache Spark 2 gives you an introduction to Apache Spark and shows you how to work with it. Along the way, you’ll discover resilient distributed datasets (RDDs); use Spark SQL for structured data; and learn stream processing and build real-time applications with Spark Structured Streaming. Furthermore, you’ll learn the fundamentals of Spark ML for machine learning and much more. After you read this book, you will have the fundamentals to become proficient in using Apache Spark and know when and how to apply it to your big data applications. You will: Understand Spark unified data processing platform Use and manipulate RDDs Deal with structured data using Spark SQL Build real-time applications using Spark Structured Streaming Develop intelligent applications with the Spark Machine Learning library.Beginning Apache Spark twoBig dataJava (Computer program language)Data miningOpen source softwareComputer programmingBig Datahttps://scigraph.springernature.com/ontologies/product-market-codes/I29120Javahttps://scigraph.springernature.com/ontologies/product-market-codes/I29070Data Mining and Knowledge Discoveryhttps://scigraph.springernature.com/ontologies/product-market-codes/I18030Open Sourcehttps://scigraph.springernature.com/ontologies/product-market-codes/I29090Big data.Java (Computer program language)Data mining.Open source software.Computer programming.Big Data.Java.Data Mining and Knowledge Discovery.Open Source.005.7Luu Hienauthttp://id.loc.gov/vocabulary/relators/aut1060685UMIUMIBOOK9910300752003321Beginning Apache Spark 22514874UNINA