Several Theorems on Single and Set-Valued Prešić Type Mappings

Abstract

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Prešić type almost F-contractive operators is not included in Prešić type class of set-valued Prešić type almost contractive operators.

On F-Contractions: A Survey

“…The set-valued (α − φ)-Fcontraction mappings in the setting of a partial metric space are introduced in [103]. Further, multivalued F-contractions in 0-complete partial metric spaces are studied in [104]; common fixed point theorems for a pair of multivalued mappings satisfying a new Ćirić-type rational F-contraction condition in complete dislocated metric spaces in [105]; some fixed point theorems, coincidence point theorems and common fixed point theorems for multivalued F-contractions involving a binary relation that is not necessarily a partial order, in the context of generalized metric spaces (in the sense of Jleli and Samet) in [106]; fixed point results for closed multivalued F-contractions or multivalued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces in [107]; set-valued G-Prešić type F-contractions on product spaces when the underlying space is a complete metric space endowed with a graph in [108]; generalized dynamic process for generalized multivalued F-contraction of Hardy-Rogers type in b-metric spaces is discussed in [109], while the set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space are introduced in [110].…”