Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application

Abstract

The purpose of this paper is to introduce the notion of generalized multivalued ψ , ϕ -type contractions and generalized multivalued ψ , ϕ -type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented.

On Certain Applications via (𝜑, ℘) -Suzuki type Fixed Point Results in 𝐴𝑏-Metric Spaces

“…Generalized versions of the core discoveries of Banach and Edelstein were recently shown by Suzuki (1) which sparked a great deal of interest in this area (2)(3)(4) . The notion of b-Metric Space (MS) was proposed (5) in 1989.…”

Results on fixed circles and discs for $L_{ (\omega,C ) }$-contractions and related applications

“…Recently, Ameer [36] introduced common fixed point results for generalized multivalued (α * K , ϒ, )-contractions in α K -complete partial b-metric spaces. Moreover, Ameer [37,38] introduced common fixed point results for generalized multivalued (ϒ, )-contractions in complete metric and b-metric spaces. Ameer et al [39] initiated the notion of rational ( , ϒ, )-contractive pair of mappings (where is a binary relation) and established new common fixed point results for these mappings in complete metric spaces, see also ([40, 41]).…”

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

“…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. Ameer et al [6] initiated the notion of rational (Υ, Λ, )-contractive pair of mappings (where is a binary relation) and established new common fixed point results for these mappings in complete metric spaces.…”