Statistical Convergence of Sequences, Series, and Measurable Functions with Application in Fourier Series

Abstract

The dissertation entitled as "Statistical Convergence of Sequences, Series and Measurable functions with applications in Fourier Series", encompasses a concise description of inquisition prosecute by numerous researchers. Besides this certain results are evinced on statistical convergence under the enlightenment of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, Thapar Institute of Engineering and Technology, Patiala. Currently, the dissertation presents four chapters along with the conclusion. Chapter I is the introductory which includes certain well known results, examples and assertions and comparison of Statistical convergence with classical convergence. The objective of Chapter II and III is to study the convergence of single and multiple sequences and series statistically already explained by Ferenc M oricz and evaluating certain results and remarks. In Chapter IV, the statistical limit of measurable function at 1 is explained with hypothesis and assertions with application to Fourier Transform. Towards the end, references of various publications cited in the current dissertation have been reported.