![]() ![]() The main aim of this paper is to introduce the weighted geometric mean method of convergence for sequences in R + by using multiplicative calculus and prove related convergence theorems in R + with application to intuitionistic fuzzy number space. To recover the convergence of such sequences, we need new types-methods of convergence. Besides, in some cases, the limit may not be unique or may not be the intended value even if the convergence is achieved via those types of convergence. There are many examples of sequences in real number space and in intuitionistic fuzzy number space where the convergence can not be achieved via existing types of convergence. ![]() In particular, see intuitionistic fuzzy aggregation operators. By the way, weighted geometric means are encountered in many topics of mathematics one of which is sequences of IFNs. In this paper, we use multiplicative calculus to deal with the convergence of sequences of real numbers through weighted geometric means. Being the main concept of this paper, the convergence of sequences of positive real numbers is also defined via these operations in multiplicative calculus. The operations multiplication and division are crucial in multiplicative calculus and many concepts such as differentiation and integration are based on these operations. Multiplicative calculus is alternative to classical calculus and uses ratios instead of differences in order to measure deviations and compare numbers.
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