In this paper, we introduce two dimensional difference operator and its inverse by which we obtain two dimensional Fibonacci sequence and its sum. Some theorems and interesting results on the sum of the terms of two dimensional Fibonacci sequence are derived. Suitable examples are provided to illustrate our results.

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Abstract:The main objective of this paper is nding new types of discrete transforms with tuning factor t. This is not only analogy to the continuous Laplace transform but gives discrete Laplace-Fibonacci transform (LF t ). This type of Laplace-Fibonacci transform is not available in the continuous case. The LF t generates uncountably many outcomes when the parameter t varies on ( , ∞). This possibility is not available in the existing Laplace transform. All the formulae and results derived are veri ed by MATLAB.