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The development of the study of sequence spaces got momentum by the introduction of new convergence methods. Some of them are statistical convergence, lacunary convergence, lacunary statistical convergence etc.In the thesis, I have basically concentrated on various type of convergence methods and developed new classes of statistical and lacunary convergent sequences by using Orlicz and Modulus functions. We have also introduced these convergence methods in the space of vector valued double difference sequences. The concept of statistical convergence which is defined for locally convex...