Statistical deferred weighted [Formula: see text]-summability and its applications to associated approximation...

Area of Science:

• Mathematical Analysis
• Approximation Theory
• Functional Analysis

Background:

• Introduces statistical weighted lambda-summability (Kadak et al., 2017).
• Builds upon existing concepts in summability theory and approximation theorems.
• Addresses the need for advanced convergence methods in functional analysis.

Purpose of the Study:

• To investigate statistical deferred weighted lambda-summability and deferred weighted lambda-statistical convergence.
• To establish an inclusion relation between these two novel convergence concepts.
• To develop a new Korovkin-type approximation theorem for functions of two variables in a Banach space.

Main Methods:

• Introduced and defined statistical deferred weighted lambda-summability and deferred weighted lambda-statistical convergence.
• Established theoretical inclusion relations between the defined convergence types.
• Utilized the modulus of continuity to analyze the rate of convergence.

Main Results:

• Established a novel Korovkin-type approximation theorem for functions of two variables in a Banach space.
• Demonstrated that the new theorem is a significant extension of existing approximation theorems.
• Derived a result concerning the rate of deferred weighted lambda-statistical convergence.

Conclusions:

• The study successfully introduced and analyzed new concepts in summability theory.
• The developed Korovkin-type theorem offers a generalized approach to function approximation.
• The findings provide a valuable contribution to the field of approximation theory and functional analysis.