# Fixed point results in intuitionistic fuzzy pentagonal controlled metric spaces with applications to dynamic market equilibrium and satellite web coupling

## TL;DR

This paper introduces a new mathematical space and applies it to model uncertainty in dynamic markets and satellite web coupling.

## Contribution

The paper introduces intuitionistic fuzzy pentagonal controlled metric spaces and proves the Banach fixed point theorem in this context.

## Key findings

- Intuitionistic fuzzy pentagonal controlled metric spaces generalize existing fuzzy metric spaces.
- The Banach fixed point theorem is proven in this new space, supporting non-trivial examples.
- Applications to dynamic market equilibrium and satellite web coupling are demonstrated.

## Abstract

This manuscript contains several new spaces as the generalizations of fuzzy triple controlled metric space, fuzzy controlled hexagonal metric space, fuzzy pentagonal controlled metric space and intuitionistic fuzzy double controlled metric space. We prove the Banach fixed point theorem in the context of intuitionistic fuzzy pentagonal controlled metric space, which generalizes the previous ones in the existing literature. Further, we provide several non-trivial examples to support the main results. The capacity of intuitionistic fuzzy pentagonal controlled metric spaces to model hesitation, capture dual information, handle imperfect information, and provide a more nuanced representation of uncertainty makes them important in dynamic market equilibrium. In the context of changing market dynamics, these aspects contribute to a more realistic and flexible modelling approach. We present an application to dynamic market equilibrium and solve a boundary value problem for a satellite web coupling.