Higher Order Strongly m-convex Functions

Muhammad Aslam Noor () and Khalida Inayat Noor ()
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Muhammad Aslam Noor: COMSATS University Islamabad
Khalida Inayat Noor: COMSATS University Islamabad

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 319-339 from Springer

Abstract: Abstract Some new concepts of the m-convex functions, where m ∈ (0, 1] are introduced and studied. Basic properties of m-convex functions are discussed. New modified Regula Falsi methods are suggested for solving nonlinear equations. Characterizations of the higher order strongly m-convex functions are investigated under suitable conditions. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher order strongly m-convex functions. Results obtained in this paper can be viewed as refinement and significant improvement of previously known results.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_14

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DOI: 10.1007/978-3-030-72563-1_14

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