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Smoothness of Function in Terms of Kernel and Its Relation With K-Derivative

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  • Suranjana Deb

Abstract

We define a kernel function and K-derivative of a function w.r.t. this Kernel is introduced and studied, this new derivative is obtained by replacing e−st in Laplace derivative with Ks,t, the newly defined kernel. Symmetric K-derivative is defined in a way analogous to symmetric Laplace derivative. Here, in this particular piece of work, a new kind of smoothness, called K-smoothness, is defined for a function f using the kernel and the inter-relation of characteristics of f, K-derivative as well as symmetric K-derivative of f w.r.t. this kernel and its K-smoothness is discovered.

Suggested Citation

  • Suranjana Deb, 2025. "Smoothness of Function in Terms of Kernel and Its Relation With K-Derivative," Journal of Mathematics, Hindawi, vol. 2025, pages 1-8, March.
    • Handle: RePEc:hin:jjmath:6629509
    DOI: 10.1155/jom/6629509
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