Applications to Boundary Value Problems and Homotopy Theory via Tripled Fixed Point Techniques in Partially Metric Spaces

Abstract

In this manuscript, some tripled fixed point results were derived under (φ,ρ,ℓ)-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, some results about a homotopy results are obtained. Finally, theoretical results are involved in some applications, such as finding the unique solution to the boundary value problems and homotopy theory.

Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators

“…Due to the ease of this principle and its essence, which is related to many applications in various branches of mathematics, many researchers have created various supplements and additions. For example, see [2][3][4][5][6][7][8].…”

Existence of Unique Solution of Urysohn and Fredholm Integral Equations in Complex Double Controlled Metric Type Spaces

“…ose considered rational type contractions are themselves, in fact, generalizations of Banach contraction principle. For more studies, refer to [6][7][8][9][10][11].…”

Untitled

“…The well-known fixed point finding, often known as the Banach contraction principle, is one of the most significant outcomes of mathematical analysis [1]. It is the most often used fixed point result in various disciplines of mathematics and is generalizable in a wide range of ways (see [2,3,4]). The fixed point result was defined in the context of whole metric spaces by Wardowski [5], who generalized the Banach contraction principle in metric spaces.…”

“…In particular, generalized metric spaces were introduced by Branciari [12] , in such a way that triangle inequality is replaced by the rectangular inequality d(x, y) ≤ d(x, u) + d(u, v) + d(v, y), for all pairwise distinct points x, y, u, v. Any metric space is a generalized metric space but in general, generalized metric space might not be a metric space. Various fixed point results were established on such spaces, the readers can refer to (see [13,14,15,16,17,18,19]).…”