The generalized mixed type Bernoulli-Gegenbauer polynomials of order α >−1/2 are special obtained by use the generating function method. These represent an interesting mixture between two classes functions, namely Bernoulli and Gegenbauer polynomials. main purpose this paper is to discuss some their algebraic analytic properties.

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in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...