Double Controlled Metric Type Spaces and Some Fixed Point Results

Abstract

In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces.

A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b-Metric Spaces

“…The idea of generalizing metric spaces into b-metric spaces was initiated from the works of Bakhtin [11], Bourbaki [12], and Czerwik [13,14]. In [15], the notion of b-metric space was generalized further by introducing the concept of extended b-metric spaces (see also [16][17][18]) as follows: Definition 1 ( [15]). Let U be a non empty set and φ :…”

Hybrid Ćirić Type Graphic Υ,Λ-Contraction Mappings with Applications to Electric Circuit and Fractional Differential Equations

“…Shukla [10] extended the notion of a partial metric to a partial b-metric. Afterwards, numerous research articles have been dealt with fixed point theorems for various classes of single-valued and multi-valued operators in b-metric and partial b-metric spaces (see, for example, [3,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]). In this article, we shall investigate fixed points ofĆirić type rational graphic (Υ, Λ)-contraction pair mappings on partial b-metric spaces endowed with a directed graph G.…”

Generalized (σ,ξ)-Contractions and Related Fixed Point Results in a P.M.S

“…The Banach contraction principle (BCP) [1] is an applicable instrumentation to solve problems in nonlinear analysis. The BCP has been modified in variant procedures (see e.g., [2][3][4][5][6][7][8][9][10][11]). Definition 1.…”