New generalization of metric-type spaces-strong controlled

Document Type

Article

Publication Date

2-1-2023

Abstract

In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: P(s, r) <= P(s, z) + eta (z, r)P(z, r), and keeping the symmetry condition that is P(s, r) = P(r, s) for all r, s. We demonstrate the existence of the fixed point of self-mapping and its uniqueness in such spaces that satisfy linear and nonlinear contractions. Moreover, we provide three applications of results to polynomial equations of high degree, systems of linear equations, along with fractional differential equations.

Keywords

Strong b-metric space (SbMS), A double-controlled metric type, Fixed-point and strong controlled metric-type space (SCMTS)

Publication Title

Symmetry-Basel

Divisions

Science,MathematicalSciences

Volume

15

Issue

2

Publisher

MDPI

Publisher Location

ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND

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