Summability of double fourier series by nörlund methods

The aim of this study, which consists of six chapters, is to examine the sufficient conditions for quite large classes of double Nörlund matrix and double Fourier series to be summed at any point. The results examined in this study constitute significant enlargements and generalizations of the relevant studies of Y.S. Chow, K.N. Mishra and P.L. Sharma. In the first chapter, summability and contributions of double Fourier series to science are introduced. In the second chapter, the basic definitions and results used in this study are given. In the third chapter the main results and theorems obtained as a results of the study are introduced. In the fourth chapter, the formation of the Nörlund kernel, which plays a very vital role in the study, is examined. In the fifth chapter, the proof of a theorem that enables the Nörlund summability of the Fourier series for a nonnegative and nondecreasing series is studied. And finally in the sixth chapter, the proof of a theorem concerning the Nörlund summability of Fourier series for nonnegative and nonincreasing series is examined.