A Suzuki-type multivalued contraction on weak partial metric spaces and applications

Abstract

Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693–706, 2018), we introduce the concept of -type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces.

ON H+Type Multivalued Contractions and Applications in Symmetric and Probabilistic Spaces

“…Thus, from (10), we have s(a 0 , a 1 )). (11) Persisting this way, a sequence {a j } in Y is generated such that a 2j+1 ∈ Ta 2j , a 2j+2 ∈ Sa 2j+1 satisfying α(a j , a j+1 ) ≥ 1, and…”

“…All these legendary works presented fixed point theorems using the Pompeiu-Hausdorff metric. Recently, Pathak and Shahzad [10] obtained fixed point results for H + -contractions (different from set-valued contractions), see also [11,12]. One more category of fixed point results for set-valued mappings was established by Dehaish and Latif [13] without using the Hausdorff metric.…”

On (Λ,Υ,ℜ)-Contractions and Applications to Nonlinear Matrix Equations

“…The process of generalizations and improvements of the Banach Contraction Principle [1] (1922) geared up after the result of Kannan [2] in 1968, where he showed that discontinuous self-mapping has a unique fixed point, see Reference [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, Wardowski [22] introduced a nonlinear function F under the assumptions (F 1 ) − (F 3 ) (defined below) and presented a fixed point theorem for F-contractions.…”

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.…”