Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 23 Issue 4

Let { ( )} denote the New transform of the real function . Let , be a function such that { } and { } exist. { ( ) + ( )} = { ( )} + { ( ) Proof: Let , ∈ or be constant { ( ) + ( )} = 1 ∫ − ∞ 0 { (ʋ ) + (ʋ )} { ( ) + ( )} = ∫ −∞ 0 (ʋ ) + ∫ −∞ 0 (ʋ ) = { ( )} + { ( ) …(2.1 ) If the function ̅ ( ) = { } is the transform of the function ( ) then { } = 1 (1− ʋ)̅ ( ʋ 1− ʋ ) … (2.2) Proof: { } = 1 ʋ ∫ −∞ 0 ʋ (ʋ ) = 1 ʋ −(1− ʋ) (ʋ ) … (2.3) Let (1 − ʋ) = , = 1− ʋ , = 1− ʋ and put these values in eq.(2.3) { } = 1 ∫ − ∞ 0 ( ʋ 1 − ʋ ) 1 − ʋ A New Integral Transform Called “Saxena & Gupta Transform” and Relation between New Transform and other Integral Transforms 1 Year 2023 1 Frontier Research Volume XXIII Issue ersion I V ( F ) Science © 2023 Global Journals Global Journal of II. P roperties of S axena and G upta T ransform Shifting property IV N otes i) Linearty property ii)