This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics.

• Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application

• Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications

• Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges

• Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral

• Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research.