Hybrid Multivalued Type Contraction Mappings in αK-Complete Partial b-Metric Spaces and Applications

Abstract

In this paper, we initiate the notion of generalized multivalued ( α K * , Υ , Λ ) -contractions and provide some new common fixed point results in the class of α K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

“…An interesting generalization of Banach's result in the spaces endowed with graphs was given by Jachymski [5] which unifies the results of Ran and Reurings [2], Nieto and Lopez [24,25] and Edelstein [4]. Recently, Shukla and Shahzad [27] and Shahzad and Shukla [10] extended these results for single-valued and set-valued mappings in product spaces endowed with a graph-see also [28][29][30][31][32].…”

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

“…One of these generalizations corresponding to an (Υ, Λ)-contraction, has been established by [2]. Recently, Ameer et al [3] introduced common fixed point results for generalized multivalued (α * K , Υ, Λ)-contractions in α K -complete partial b-metric spaces. Ameer et al [4,5] introduced common fixed point results for generalized multivalued (Υ, Λ)contractions in complete metric, b-metric spaces.…”

“…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.…”

Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

“…Over the last decades, many researchers have focused on fixed point theory since it plays a very important role in the resolution of several mathematical models in various fields, see References [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the tools used is the well-known Banach contraction principle, which states that if (X, d) is a complete metric space and f : X −→ X is a contraction self-mapping, then f has a unique fixed point in X.…”