Some results on fixed points of α-ψ-Ciric generalized multifunctions

Abstract

In 2012, Samet, Vetro and Vetro introduced α-ψ-contractive mappings and gave some results on a fixed point of the mappings (Samet et al. in Nonlinear Anal. 75:2154-2165. In fact, their technique generalized some ordered fixed point results (see (Alikhani et al. in Filomat, 2012, to appear) and (Samet et al. in Nonlinear Anal. 75:2154-2165). By using the main idea of (Samet et al. in Nonlinear Anal. 75:2154-2165, we give some new results for α-ψ-Ciric generalized multifunctions and some related self-maps. Also, we give an affirmative answer to a recent open problem which was raised by Haghi, Rezapour and Shahzad in 2012.

Fuzzy fixed point theorems for fuzzy mappings via β-admissible with applications

“…Mohammadi et al [13]. We also give illustrative example which demonstrate the validity of hypotheses of our results.…”

“…Afterward, Asl et al [12] extended the concept of β-admissible for single-valued mappings to multivalued mappings. Recently, Mohammadi et al [13] introduced the concept of β-admissible for multivalued mappings which is different from the notion of β * -admissible which has been provided in [12]. Recently, Azam et al [14], obtained common fixed point theorems for Chatterjea fuzzy mappings on closed balls in a complete metric space.…”

Coupled Fixed Points of ?-?-Contractive Type Multi Functions

“…We say that T is α-admissible whenever for each x ∈ X and y ∈ T x with α(x, y) ≥ 1 we have α(y, z) ≥ 1 for all z∈ Ty ( [4]). Recall that T is continuous whenever H (Tx n ,Tx) → 0 for all sequence {x n } in X with x n → x, where H is the Hausdorff metric on…”

“…2 →X an α-admissible mapping such that [4] ( ) ( ) ( ) (ii) Either F is continuous or ψ is right upper semi continuous and X satisfies condition…”

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“…In 2013, Mohammadi et al [7] extended the concept of an˛ -admissible mapping to an˛-admissible mapping as follows:…”