{"product_id":"new-perspectives-on-the-theory-of-inequalities-for-integral-and-sum-9783030905651","title":"New Perspectives on the Theory of Inequalities for Integral and Sum","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003e\n\u003cbr\u003eThis book discusses new inequalities for integral and sum, including results related to Popoviciu type linear inequalities, Ostrowskis inequality, functions with nondecreasing increments, and Popoviciu and Cebysev-Popoviciu type identities and inequalities. It also presents applications to numerical integration and probability theory. \u003c\/blockquote\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 308 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 31 March 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer Nature Switzerland AG\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003eThis book is a valuable addition to the field of inequalities, particularly focusing on integral and sum inequalities. It comprises four chapters, each offering fresh insights into the theory.\u003cbr\u003e\u003cbr\u003eIn the first chapter, the authors delve into the realm of linear inequalities through the use of interpolation polynomials and green functions. They present novel results related to Popoviciu-type linear inequalities, extending the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials, and the Fink identity with Green's functions. These results showcase the power of these tools in solving inequality problems.\u003cbr\u003e\u003cbr\u003eThe second chapter is dedicated to Ostrowski's inequality, which finds applications in numerical integration and probability theory. The authors present various results related to Ostrowski's inequality, including those involving the Riemann sum and the integral transform. These results provide valuable tools for practitioners in these fields.\u003cbr\u003e\u003cbr\u003eThe third chapter explores the realm of functions with nondecreasing increments. The authors discuss real-life applications of these functions and their connection with important concepts such as the arithmetic integral mean, Wright convex functions, convex functions, nabla-convex functions, Jensen's m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, complete monotonic functions, Laplace transform, and exponentially convex functions. They employ the finite difference operator of order m to derive these results.\u003cbr\u003e\u003cbr\u003eThe fourth chapter primarily focuses on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this chapter, the authors present their findings by utilizing delta and nabla operators of higher order. These results add to the existing body of knowledge in the field and provide valuable insights for further research.\u003cbr\u003e\u003cbr\u003eOverall, this book is a must-read for anyone interested in inequalities, particularly those working in integral and sum inequalities. The comprehensive coverage of topics and the use of modern mathematical techniques make it an invaluable resource for scholars and practitioners alike.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 498g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 235 x 155 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783030905651\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2021\u003c\/p\u003e","brand":"Nazia Irshad,Asif R. Khan,Faraz Mehmood,Josip Pecaric","offers":[{"title":"Paperback \/ softback","offer_id":44307609387258,"sku":"9783030905651","price":91.62,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_e0c62824-dd98-4542-bb29-155c34a56405.jpg?v=1688110380","url":"https:\/\/shulphink.com\/products\/new-perspectives-on-the-theory-of-inequalities-for-integral-and-sum-9783030905651","provider":"Shulph Ink","version":"1.0","type":"link"}