Kannan-Type Contractions on New Extended $b$-Metric Spaces

Abstract

This article is focused on the generalization of some fixed point theorems with Kannan-type contractions in the setting of new extended b -metric spaces. An idea of asymptotic regularity has been incorporated to achieve the new results. As an application, the existence of a solution of the Fredholm-type integral equation is presented.

Some Results of Unique Common Fixed Point Generalized In Extended b_2-metric spaces

“…As a consequence, the claim is valid. Example2.3 [6,11] Remark2.2 An extended 𝑏 2 -metric 𝜌 𝜑 is generally not a continuous function of its variables(see [7] Example 2.3, for instance ). Proposition 2.1 [5] In an extended 𝑏 2 -metric space (Υ, 𝜌 𝜑 ), if 𝜌 𝜑 a continuous function, then the following assertions hold: i) The limit of converges sequence is unique, ii) any subsequence of a sequence {𝜒 𝑟 } that converges as well.…”

The uniqueness and existence of solutions in a new complex function space for Kannan nonlinear dynamical systems

“…In addition, several fixed point findings of Kannan non-expansive operators on generalized Cesàro backward difference sequence space of a non-absolute type were discovered in [7]. Among the Kannan fixed point results, we refer the reader to Gaba et al [17] and Aydi et al [3]. By N, R, and C, we will indicate the sets of non-negative integers, real and complex numbers, respectively.…”

Fixed Point Results for Single and Multivalued Maps on Partial Extended b -Metric Spaces

“…A lot of research can be seen in literature on b-metric spaces (see [1,2,7,8,[19][20][21][22][23]), which is a stimulation towards the concept of extended b-metric spaces introduced by Kamran et al [6] who proved the Banach contraction theorem in the setting of extended b-metric spaces. Afterwards, many authors have focused on the subject and generalized different results of metric spaces in extended b-metric spaces (see [3,[24][25][26][27][28]). Very recently, Aydi et al [5] have introduced the concept of new extended b-metric spaces by replacing the triangle inequality of extended b-metric spaces with a modified functional inequality.…”