An Approach to Existence of Fixed Points of Generalized Contractive Multivalued Mappings of Integral Type via Admissible Mapping

Abstract

We investigate the existence of a fixed point of certain contractive multivalued mappings of integral type by using the admissible mapping. Our results generalize the several results on the topic in the literature involving Branciari, and Feng and Liu. We also construct some examples to illustrate our results.

Fixed Points Results forα-Admissible Mapping of Integral Type on Generalized Metric Spaces

“…Example 13 (see [29]). Let 1 ( ) = (1/2)( +1) −1/2 for all ≥ 0, In what follows we introduce notions of generalized − -contractive type mappings of integral type I and type II.…”

A fixed point theorem for generalized contractive type set-valued mappings with application to nonlinear fractional differential inclusions

“…Let T be defined as (9). It is easy to check, fixed points of T are solutions of problem (8). Suppose that x 1 , x 2 ∈ C(J, R) and h 1 ∈ T(x 1 ) so there exists 1 ∈ S F,x 1 such that for each t ∈ J…”

“…Moreover, since F is compact valued and F(t, 0) ⊂ l(t)B(0, 1), we can prove that T has compact values too. Thus, Corollary 2.5 can be applied for T and so there exists x * ∈ X such that x * ∈ T(x * ) and x * is a solution of problem (8). We set ψ(t) = 1 2 t and l(t) = 7 23 (t + 2) for each t ∈ [0, ∞).…”

On the weakly(α, ψ, ξ)-contractive condition for multi-valued operators in metric spaces and related fixed point results

“…For more details of fixed point results and recently related results by using the concepts of˛-admissible single valued and˛-admissible multi-valued mappings, one can refer to [8][9][10][11][12][13][14][15][16] and references therein.…”