Executive Summary : | The Ph.D. thesis focuses on the generalized difference lacunary weak convergence of sequences, the second order difference quantum difference operator, lacunary weak convergence of sequences defined by Orlicz function, lacunary statistically weak convergence of difference sequences, and lacunary weak ideal convergence of sequences. The thesis investigates the properties of lacunary sequences, including solidness, symmetry, monotonicity, and convergence freedom. The research will involve constructing lacunary weak convergent sequence spaces, lacunary weak null, weak Cesa ̀ro summable, and weak almost convergent sequences, and examining the relationship between lacunary strong convergent sequences and lacunary weak convergent sequences. The work plan includes passing the course work examination, preparing for literature review, preparing articles for journal publication, presenting results at conferences and workshops, and preparing the thesis for evaluation by adjudicators. |